Pub Date : 2025-09-26DOI: 10.1016/j.wavemoti.2025.103644
Wen-Xiu Ma
Starting from the matrix AKNS spectral problem, we construct a Lax pair featuring a first-order non-zero pole in the spectral parameter and derive a matrix generalization of the Kuralay-II equation. The associated Darboux transformation is developed within the AKNS framework. By applying this transformation to a non-zero seed solution, we obtain a class of exact and explicit solutions.
{"title":"Matrix extension of the Kuralay-II Equation and its associated Darboux transformation","authors":"Wen-Xiu Ma","doi":"10.1016/j.wavemoti.2025.103644","DOIUrl":"10.1016/j.wavemoti.2025.103644","url":null,"abstract":"<div><div>Starting from the matrix AKNS spectral problem, we construct a Lax pair featuring a first-order non-zero pole in the spectral parameter and derive a matrix generalization of the Kuralay-II equation. The associated Darboux transformation is developed within the AKNS framework. By applying this transformation to a non-zero seed solution, we obtain a class of exact and explicit solutions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103644"},"PeriodicalIF":2.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-20DOI: 10.1016/j.wavemoti.2025.103642
Sophie Thery , Malte A. Peter , Luke G. Bennetts , Sébastien Guenneau
The principle of cloaking has been developed and applied to different types of waves. We consider the application in the context of flexural–gravity waves on shallow water in order to reduce the wave force on an object. The parameters of the plate used to create a cloak in the vicinity of the object are found applying a space transformation method to the wave-propagation equation. The governing equation of a Kirchhoff–Love plate is generally not shape-invariant, which traditionally induces error terms in the (thus approximate) use of the space transformation method. First deriving the equations of motion for the shallow-water–fully anisotropic plate system by a variational principle, we extend the transformation method to anisotropic plates and show that for every change of coordinates there exists a class of anisotropic plates such that the equation of motion is shape-invariant. Furthermore, we consider examples in which the wave force on and the scattering by a rigid bottom-mounted vertical cylinder are reduced when surrounded by a floating plate with a cloaking region having material parameters computed by the presented method and we illustrate an approximate case by simulations.
{"title":"Transformation-based cloaking for flexural–gravity waves in an anisotropic plate floating on shallow water","authors":"Sophie Thery , Malte A. Peter , Luke G. Bennetts , Sébastien Guenneau","doi":"10.1016/j.wavemoti.2025.103642","DOIUrl":"10.1016/j.wavemoti.2025.103642","url":null,"abstract":"<div><div>The principle of cloaking has been developed and applied to different types of waves. We consider the application in the context of flexural–gravity waves on shallow water in order to reduce the wave force on an object. The parameters of the plate used to create a cloak in the vicinity of the object are found applying a space transformation method to the wave-propagation equation. The governing equation of a Kirchhoff–Love plate is generally not shape-invariant, which traditionally induces error terms in the (thus approximate) use of the space transformation method. First deriving the equations of motion for the shallow-water–fully anisotropic plate system by a variational principle, we extend the transformation method to anisotropic plates and show that for every change of coordinates there exists a class of anisotropic plates such that the equation of motion is shape-invariant. Furthermore, we consider examples in which the wave force on and the scattering by a rigid bottom-mounted vertical cylinder are reduced when surrounded by a floating plate with a cloaking region having material parameters computed by the presented method and we illustrate an approximate case by simulations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103642"},"PeriodicalIF":2.5,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-13DOI: 10.1016/j.wavemoti.2025.103633
Wentao Li , Zhao Zhang , Biao Li
The Lakshmanan–Porsezian–Daniel (LPD) equation describes the effect of biquadratic interactions on the integrable properties of Heisenberg bilinear spin chains in the classical limit. By applying multiple-scale method, the Korteweg–de Vries (KdV) equation and a generalized fifth-order KdV equation are derived from the LPD equation. Based on the perturbation analysis, asymptotic one- and two-soliton solutions are constructed. The dispersive terms in the KdV and generalized fifth-order KdV equation provide the leading-order and higher-order corrections to the soliton velocities, respectively. Furthermore, the corresponding numerical solutions are obtained by imposing suitable periodic boundary conditions on the asymptotic one- and two-soliton solutions and applying the Fourier spectral method. The good agreement between the numerical results and the asymptotic solutions confirms the validity of the constructed solution for the LPD equation.
{"title":"Asymptotic analysis on a Lakshmanan–Porsezian–Daniel equation in nonlinear optics","authors":"Wentao Li , Zhao Zhang , Biao Li","doi":"10.1016/j.wavemoti.2025.103633","DOIUrl":"10.1016/j.wavemoti.2025.103633","url":null,"abstract":"<div><div>The Lakshmanan–Porsezian–Daniel (LPD) equation describes the effect of biquadratic interactions on the integrable properties of Heisenberg bilinear spin chains in the classical limit. By applying multiple-scale method, the Korteweg–de Vries (KdV) equation and a generalized fifth-order KdV equation are derived from the LPD equation. Based on the perturbation analysis, asymptotic one- and two-soliton solutions are constructed. The dispersive terms in the KdV and generalized fifth-order KdV equation provide the leading-order and higher-order corrections to the soliton velocities, respectively. Furthermore, the corresponding numerical solutions are obtained by imposing suitable periodic boundary conditions on the asymptotic one- and two-soliton solutions and applying the Fourier spectral method. The good agreement between the numerical results and the asymptotic solutions confirms the validity of the constructed solution for the LPD equation.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103633"},"PeriodicalIF":2.5,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-11DOI: 10.1016/j.wavemoti.2025.103626
Maria Carrillo-Munoz, Anwaruddin Siddiqui Mohammed, Bhisham Sharma
We investigate the elastic wave dispersion of surface-based gyroid lattices and analyze how introducing material and geometric asymmetry affects their behavior. First, we show that unmodified (high-symmetry) gyroid lattices exhibit multiple degeneracies in their dispersion relations, preventing bandgap formation. To lift these degeneracies, we implement two asymmetry strategies: (1) Material asymmetry, by assigning different stiffness or density to distinct regions of the unit cell; and (2) Geometric asymmetry, by scaling the lattice unequally along coordinate axes to create anisotropic “gyroid-derived” shapes. Bloch–Floquet analysis of the infinite periodic lattices reveals that both approaches open new bandgaps. Material-asymmetric gyroids develop polarized-directional bandgaps that block one shear polarization in specific directions, and for moderate stiffness or density contrast, produce a “fluid-like” regime in which both shear polarizations ( and ) are strongly attenuated, allowing only longitudinal () waves. Geometrically asymmetric gyroids likewise exhibit directional bandgaps and, at low frequencies, display anomalous propagation: shear wave phase velocities exceed longitudinal wave velocities—a reversal of the usual hierarchy. Computational homogenization confirms that these anomalies arise from anisotropic effective stiffness coefficients and surpassing along certain axes. Overall, our results demonstrate that deliberate material or geometric asymmetry in gyroid lattices enables precise tailoring of bandgaps and wave-speed hierarchies, offering an effective approach for the design of architected metamaterials for vibration isolation and wave control.
{"title":"Symmetry breaking induces polarized bandgaps and anomalous elastic wave behavior in gyroid lattices","authors":"Maria Carrillo-Munoz, Anwaruddin Siddiqui Mohammed, Bhisham Sharma","doi":"10.1016/j.wavemoti.2025.103626","DOIUrl":"10.1016/j.wavemoti.2025.103626","url":null,"abstract":"<div><div>We investigate the elastic wave dispersion of surface-based gyroid lattices and analyze how introducing material and geometric asymmetry affects their behavior. First, we show that unmodified (high-symmetry) gyroid lattices exhibit multiple degeneracies in their dispersion relations, preventing bandgap formation. To lift these degeneracies, we implement two asymmetry strategies: (1) Material asymmetry, by assigning different stiffness or density to distinct regions of the unit cell; and (2) Geometric asymmetry, by scaling the lattice unequally along coordinate axes to create anisotropic “gyroid-derived” shapes. Bloch–Floquet analysis of the infinite periodic lattices reveals that both approaches open new bandgaps. Material-asymmetric gyroids develop polarized-directional bandgaps that block one shear polarization in specific directions, and for moderate stiffness or density contrast, produce a “fluid-like” regime in which both shear polarizations (<span><math><mi>S</mi></math></span> <span><math><msub><mrow></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mi>S</mi></math></span> <span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span>) are strongly attenuated, allowing only longitudinal (<span><math><mi>P</mi></math></span>) waves. Geometrically asymmetric gyroids likewise exhibit directional bandgaps and, at low frequencies, display anomalous propagation: shear wave phase velocities exceed longitudinal wave velocities—a reversal of the usual hierarchy. Computational homogenization confirms that these anomalies arise from anisotropic effective stiffness coefficients <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>44</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>66</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> surpassing <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mn>11</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></math></span> along certain axes. Overall, our results demonstrate that deliberate material or geometric asymmetry in gyroid lattices enables precise tailoring of bandgaps and wave-speed hierarchies, offering an effective approach for the design of architected metamaterials for vibration isolation and wave control.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103626"},"PeriodicalIF":2.5,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-04DOI: 10.1016/j.wavemoti.2025.103632
Biao Li , Yongyan Zhang , Xiangjie Miao , Zebo Zhao , Liming Chen , Hui Liu
In this paper, we propose a lightweight helical plate elastic metamaterial with gradient springs for low-frequency vibration suppression, leveraging the local resonance effect of helical gradient springs to achieve both an ultra-wide complete bandgap and a bending wave bandgap in the low-frequency range. Theoretical analysis and finite element simulations reveal the critical role of helical gradient springs in stiffness tuning and the local resonance mechanism. By integrating multiple pitches and radii, the design offers greater flexibility in stiffness adjustment compared with conventional single-pitch and single-radius springs. This enables the realization of negative stiffness characteristics and allows more flexible optimization of the bandgap range and performance. Moreover, adjusting the number of helical gradient spring arrays further enhances the bandgap width, system stability, and lightweight properties. After determining suitable geometric parameters through parametric analysis, the proposed structure achieves bending wave bandgaps from 29 Hz to 454 Hz and a complete bandgap from 72 Hz to 436 Hz, both representing ultra-wide low-frequency ranges. Additionally, intrinsic modal analysis and transmission spectrum characterization elucidate the physical mechanisms of bandgap formation and validate the design. This helical gradient spring-based local resonance structure addresses the challenges posed by the high mass and volume of traditional phononic crystals, offering a promising approach for engineering applications in low-frequency acoustic isolation metamaterials.
{"title":"A lightweight helical plate elastic metamaterial for low-frequency vibration suppression","authors":"Biao Li , Yongyan Zhang , Xiangjie Miao , Zebo Zhao , Liming Chen , Hui Liu","doi":"10.1016/j.wavemoti.2025.103632","DOIUrl":"10.1016/j.wavemoti.2025.103632","url":null,"abstract":"<div><div>In this paper, we propose a lightweight helical plate elastic metamaterial with gradient springs for low-frequency vibration suppression, leveraging the local resonance effect of helical gradient springs to achieve both an ultra-wide complete bandgap and a bending wave bandgap in the low-frequency range. Theoretical analysis and finite element simulations reveal the critical role of helical gradient springs in stiffness tuning and the local resonance mechanism. By integrating multiple pitches and radii, the design offers greater flexibility in stiffness adjustment compared with conventional single-pitch and single-radius springs. This enables the realization of negative stiffness characteristics and allows more flexible optimization of the bandgap range and performance. Moreover, adjusting the number of helical gradient spring arrays further enhances the bandgap width, system stability, and lightweight properties. After determining suitable geometric parameters through parametric analysis, the proposed structure achieves bending wave bandgaps from 29 Hz to 454 Hz and a complete bandgap from 72 Hz to 436 Hz, both representing ultra-wide low-frequency ranges. Additionally, intrinsic modal analysis and transmission spectrum characterization elucidate the physical mechanisms of bandgap formation and validate the design. This helical gradient spring-based local resonance structure addresses the challenges posed by the high mass and volume of traditional phononic crystals, offering a promising approach for engineering applications in low-frequency acoustic isolation metamaterials.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103632"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.wavemoti.2025.103630
Jiguang Rao , Dumitru Mihalache , Minjie Ma , Jingsong He
This study delves into the asymptotic analysis and dynamics of multi-breather waveforms within the nonlocal space-shifted nonlinear Schrödinger equation on two distinct backgrounds: a continuous background represented by a plane wave, and a periodic background with periodicity solely along the spatial variable. These breathers are grouped into multiple pairs during the asymptotic analysis, wherein the speeds of two breathers are identical but opposite in directions. Our analysis reveals that the shifting parameter significantly influences the localization center of only one breather within each breather pair in space. The other breather in each pair remains unaffected by changes in , except for the shifts in the position of the maximum amplitude point of this breather on the spatial periodic background. By scrutinizing the correlations between velocities or periodicities and the corresponding amplitudes, we uncover both similarities and differences between nonlocal breathers and their associated local counterparts. While both types of breathers exhibit identical relations between velocities or periodicities and their associated parameters, the relationship between amplitude and its parameters for local breathers represents a specific example within the broader spectrum observed in the case of nonlocal breathers. Hence, the correlations of velocities or periodicities with amplitudes for local breathers are considered a subset of those observed in nonlocal breathers. The findings shed light on the intricate dynamics of multi-breather waveforms, offering valuable insights into their behavior on different backgrounds.
{"title":"The asymptotic analysis to multi-breather solutions of the nonlocal space-shifted nonlinear Schrödinger equation on continuous and spatial periodic backgrounds","authors":"Jiguang Rao , Dumitru Mihalache , Minjie Ma , Jingsong He","doi":"10.1016/j.wavemoti.2025.103630","DOIUrl":"10.1016/j.wavemoti.2025.103630","url":null,"abstract":"<div><div>This study delves into the asymptotic analysis and dynamics of multi-breather waveforms within the nonlocal space-shifted nonlinear Schrödinger equation on two distinct backgrounds: a continuous background represented by a plane wave, and a periodic background with periodicity solely along the spatial variable. These breathers are grouped into multiple pairs during the asymptotic analysis, wherein the speeds of two breathers are identical but opposite in directions. Our analysis reveals that the shifting parameter <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> significantly influences the localization center of only one breather within each breather pair in space. The other breather in each pair remains unaffected by changes in <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, except for the shifts in the position of the maximum amplitude point of this breather on the spatial periodic background. By scrutinizing the correlations between velocities or periodicities and the corresponding amplitudes, we uncover both similarities and differences between nonlocal breathers and their associated local counterparts. While both types of breathers exhibit identical relations between velocities or periodicities and their associated parameters, the relationship between amplitude and its parameters for local breathers represents a specific example within the broader spectrum observed in the case of nonlocal breathers. Hence, the correlations of velocities or periodicities with amplitudes for local breathers are considered a subset of those observed in nonlocal breathers. The findings shed light on the intricate dynamics of multi-breather waveforms, offering valuable insights into their behavior on different backgrounds.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103630"},"PeriodicalIF":2.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.wavemoti.2025.103631
Ana L. Ramos-Barreto , Tobias M. Müller , Rubén Rioyos-Romero , Jonas D. De Basabe
Understanding how fractures and fluids can influence elastic-wave propagation remains a complex puzzle, driving the exploration of the relationship between fluid properties and P-wave propagation through fractured media. Unraveling fluid viscosity and density from P-wave recordings still poses challenges, and the literature does not provide univocal answers. Therefore, we conduct both laboratory and numerical experiments to examine the effects of fluid viscosity and density on P-wave propagation when fractures are interpreted in terms of the linear-slip model. The medium consists of stacked aluminum discs with parallel horizontal fractures. We consider 1, 5 and 10 fractures and use water, silicone oil and honey as infill materials. In the laboratory, we obtain the static and dynamic, normal and tangential compliances of parallel fluid-filled fractures. We performed numerical simulations using the discontinuous Galerkin method, incorporating the dynamic compliances obtained from the experiments. Our laboratory findings indicate that fluid density correlates positively with P-wave velocity, transmission coefficient, and quality factor. Furthermore, there is an inverse correlation with the number of fractures. In addition, the normal and tangential fracture compliances and their ratio vary between dry and saturated conditions and decrease when the number of fractures increases. The static compliance is, in general, higher than the dynamic. The numerical results showed good agreement in discriminating between different fluids, although numerical attenuation was slightly underestimated compared to experimental observations. The results highlight the impact of fluid properties on wave behavior in fractured media and provide insights into wave sensitivity to fracture characteristics.
{"title":"Laboratory and numerical experiments of wave propagation in media with fluid-filled fractures","authors":"Ana L. Ramos-Barreto , Tobias M. Müller , Rubén Rioyos-Romero , Jonas D. De Basabe","doi":"10.1016/j.wavemoti.2025.103631","DOIUrl":"10.1016/j.wavemoti.2025.103631","url":null,"abstract":"<div><div>Understanding how fractures and fluids can influence elastic-wave propagation remains a complex puzzle, driving the exploration of the relationship between fluid properties and P-wave propagation through fractured media. Unraveling fluid viscosity and density from P-wave recordings still poses challenges, and the literature does not provide univocal answers. Therefore, we conduct both laboratory and numerical experiments to examine the effects of fluid viscosity and density on P-wave propagation when fractures are interpreted in terms of the linear-slip model. The medium consists of stacked aluminum discs with parallel horizontal fractures. We consider 1, 5 and 10 fractures and use water, silicone oil and honey as infill materials. In the laboratory, we obtain the static and dynamic, normal and tangential compliances of parallel fluid-filled fractures. We performed numerical simulations using the discontinuous Galerkin method, incorporating the dynamic compliances obtained from the experiments. Our laboratory findings indicate that fluid density correlates positively with P-wave velocity, transmission coefficient, and quality factor. Furthermore, there is an inverse correlation with the number of fractures. In addition, the normal and tangential fracture compliances and their ratio vary between dry and saturated conditions and decrease when the number of fractures increases. The static compliance is, in general, higher than the dynamic. The numerical results showed good agreement in discriminating between different fluids, although numerical attenuation was slightly underestimated compared to experimental observations. The results highlight the impact of fluid properties on wave behavior in fractured media and provide insights into wave sensitivity to fracture characteristics.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103631"},"PeriodicalIF":2.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-30DOI: 10.1016/j.wavemoti.2025.103617
Guoqiang Li, Pei Zheng, Keming Zhang
In this paper, propagation of Rayleigh waves in a fluid-saturated porous solid is studied by using the couple-stress-based gradient theory, which incorporates the rotation gradient, and its work-conjugate counterpart, the couple-stress. In the frequency domain, wave equations involving a length parameter , that characterizes the microstructure of the material, are derived and, by using displacement potentials, coupled wave equations are reduced to four uncoupled wave equations governing the motions of -, -, -, and -waves. Based on the solutions of these equations, the dispersion equation for Rayleigh waves is obtained. Numerical results show that Rayleigh waves are dispersive at all frequencies in the range considered, unlike the velocity dispersion characterized by the classical theory, and the wave velocity is always higher than the conventional Rayleigh wave velocity. It is shown that the attenuation decreases as increases. The effects of porosity, the ratio of bulk modulus of the solid skeleton to the solid phase, and the length parameter on Rayleigh wave dispersion and attenuation are also investigated.
{"title":"Rayleigh wave dispersion and attenuation characterized by couple-stress-based poroelasticity","authors":"Guoqiang Li, Pei Zheng, Keming Zhang","doi":"10.1016/j.wavemoti.2025.103617","DOIUrl":"10.1016/j.wavemoti.2025.103617","url":null,"abstract":"<div><div>In this paper, propagation of Rayleigh waves in a fluid-saturated porous solid is studied by using the couple-stress-based gradient theory, which incorporates the rotation gradient, and its work-conjugate counterpart, the couple-stress. In the frequency domain, wave equations involving a length parameter <span><math><mi>ℓ</mi></math></span>, that characterizes the microstructure of the material, are derived and, by using displacement potentials, coupled wave equations are reduced to four uncoupled wave equations governing the motions of <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-, <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-, <span><math><mrow><mi>S</mi><mi>V</mi></mrow></math></span>-, and <span><math><mrow><mi>S</mi><mi>H</mi></mrow></math></span>-waves. Based on the solutions of these equations, the dispersion equation for Rayleigh waves is obtained. Numerical results show that Rayleigh waves are dispersive at all frequencies in the range considered, unlike the velocity dispersion characterized by the classical theory, and the wave velocity is always higher than the conventional Rayleigh wave velocity. It is shown that the attenuation decreases as <span><math><mi>ℓ</mi></math></span> increases. The effects of porosity, the ratio of bulk modulus of the solid skeleton to the solid phase, and the length parameter on Rayleigh wave dispersion and attenuation are also investigated.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103617"},"PeriodicalIF":2.5,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-30DOI: 10.1016/j.wavemoti.2025.103611
Chenxi Li , Xiaochuan Liu , Bao-Feng Feng
In this paper, we study the coupled complex modified Korteweg–de Vries (ccmKdV) equation by combining the Hirota’s method and the Kadomtsev–Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under nonzero boundary condition is linked to the discrete BKP hierarchy through Miwa transformation. Based on this finding, we construct the dark–dark soliton solution in the pfaffian form. The dynamical behaviors for one- and two-soliton are analyzed and illustrated.
{"title":"Pfaffian solution for dark–dark soliton to the coupled complex modified Korteweg–de Vries equation","authors":"Chenxi Li , Xiaochuan Liu , Bao-Feng Feng","doi":"10.1016/j.wavemoti.2025.103611","DOIUrl":"10.1016/j.wavemoti.2025.103611","url":null,"abstract":"<div><div>In this paper, we study the coupled complex modified Korteweg–de Vries (ccmKdV) equation by combining the Hirota’s method and the Kadomtsev–Petviashvili (KP) reduction method. First, we show that the bilinear form of the ccmKdV equation under nonzero boundary condition is linked to the discrete BKP hierarchy through Miwa transformation. Based on this finding, we construct the dark–dark soliton solution in the pfaffian form. The dynamical behaviors for one- and two-soliton are analyzed and illustrated.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103611"},"PeriodicalIF":2.5,"publicationDate":"2025-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144931881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-27DOI: 10.1016/j.wavemoti.2025.103629
Xin Wang, Zhi-hui Zhang
In this paper, a class of variable-coefficient coupled nonlinear Schrödinger equations with four-wave mixing effect is studied. Firstly, the constraint conditions that the function should satisfy when the equation is integrable are given by Painlevé analysis, and then the -soliton solution of the equation with variable coefficients was directly given by using the variable substitution technique and the Riemann–Hilbert method. On this basis, the evolution figure of the 1, 2-soliton solution was given by numerical simulation. The effects of functions and related parameters on the soliton solution dynamics are analyzed and summarized. Through our research, we can provide a certain theoretical basis for the control and application of solitons in practice.
{"title":"N-soliton solutions of four-wave mixing coupled Schrödinger equations based on Riemann–Hilbert method","authors":"Xin Wang, Zhi-hui Zhang","doi":"10.1016/j.wavemoti.2025.103629","DOIUrl":"10.1016/j.wavemoti.2025.103629","url":null,"abstract":"<div><div>In this paper, a class of variable-coefficient coupled nonlinear Schrödinger equations with four-wave mixing effect is studied. Firstly, the constraint conditions that the function should satisfy when the equation is integrable are given by Painlevé analysis, and then the <span><math><mi>N</mi></math></span>-soliton solution of the equation with variable coefficients was directly given by using the variable substitution technique and the Riemann–Hilbert method. On this basis, the evolution figure of the 1, 2-soliton solution was given by numerical simulation. The effects of functions and related parameters on the soliton solution dynamics are analyzed and summarized. Through our research, we can provide a certain theoretical basis for the control and application of solitons in practice.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103629"},"PeriodicalIF":2.5,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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