Pub Date : 2025-10-10DOI: 10.1016/j.wavemoti.2025.103649
Zhi Xin
In this paper, we study a general third-order flow equation of the Kaup-Newell system. By using the Darboux transformation method and the determinant representations of transformation and solutions, several solutions to nonlinear equations have been obtained. Including the single-periodic wave solution, soliton solution, Akhmediev breather, Kuznetsov-Ma breather and rogue wave solution. By analyzing the behavior of the above solutions, we observe that the first-order term has a rotational effect, which significantly slows down solution collision, ultimately leading to the formation of a single solution.
{"title":"An analysis of solutions derived from a general third-order flow equation of the Kaup-Newell system","authors":"Zhi Xin","doi":"10.1016/j.wavemoti.2025.103649","DOIUrl":"10.1016/j.wavemoti.2025.103649","url":null,"abstract":"<div><div>In this paper, we study a general third-order flow equation of the Kaup-Newell system. By using the Darboux transformation method and the determinant representations of transformation and solutions, several solutions to nonlinear equations have been obtained. Including the single-periodic wave solution, soliton solution, Akhmediev breather, Kuznetsov-Ma breather and rogue wave solution. By analyzing the behavior of the above solutions, we observe that the first-order <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> term has a rotational effect, which significantly slows down solution collision, ultimately leading to the formation of a single solution.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103649"},"PeriodicalIF":2.5,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333126","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 : 2025-10-10DOI: 10.1016/j.wavemoti.2025.103643
Byron Williams , Ali Abdolali , Usama Kadri
This study investigates the propagation of tsunami and acoustic–gravity waves at oceanic scales, accounting for the Earth’s curvature within a linear, potential flow framework. While local, near-field analyses often neglect Earth’s curvature and employ Cartesian or cylindrical coordinate systems, this work utilises spherical coordinates to examine wave behaviour over large distances. The analysis reveals that wave amplitudes experience a defocusing effect as they travel from the source (e.g., the Pole) toward the equator, followed by a focusing effect as they approach the antipodal point beyond the equator. A qualitative comparison is made with the 2022 Hunga Tonga–Hunga Ha’apai volcanic eruption in the South Pacific. The study models surface-gravity (tsunami) waves propagating through a compressible water layer, as well as atmospheric acoustic–gravity waves propagating through the air. The entire analysis is carried out within the framework of linear theory.
本研究调查了海啸和声重力波在海洋尺度上的传播，在线性势流框架内考虑地球的曲率。虽然局部的近场分析经常忽略地球的曲率，并使用笛卡尔或柱坐标系，但这项工作利用球坐标来检查远距离上的波的行为。分析表明，当波幅从源（例如，极点）向赤道传播时，会经历散焦效应，随后当它们接近赤道以外的对映点时，会出现聚焦效应。并与2022年南太平洋Hunga Tonga-Hunga Ha 'apai火山喷发进行了定性比较。该研究模拟了通过可压缩水层传播的表面重力（海啸）波，以及通过空气传播的大气声重力波。整个分析是在线性理论的框架内进行的。
{"title":"Linear propagation of tsunami and acoustic–gravity waves on a sphere: Geometrical focusing and defocusing","authors":"Byron Williams , Ali Abdolali , Usama Kadri","doi":"10.1016/j.wavemoti.2025.103643","DOIUrl":"10.1016/j.wavemoti.2025.103643","url":null,"abstract":"<div><div>This study investigates the propagation of tsunami and acoustic–gravity waves at oceanic scales, accounting for the Earth’s curvature within a linear, potential flow framework. While local, near-field analyses often neglect Earth’s curvature and employ Cartesian or cylindrical coordinate systems, this work utilises spherical coordinates to examine wave behaviour over large distances. The analysis reveals that wave amplitudes experience a defocusing effect as they travel from the source (e.g., the Pole) toward the equator, followed by a focusing effect as they approach the antipodal point beyond the equator. A qualitative comparison is made with the 2022 Hunga Tonga–Hunga Ha’apai volcanic eruption in the South Pacific. The study models surface-gravity (tsunami) waves propagating through a compressible water layer, as well as atmospheric acoustic–gravity waves propagating through the air. The entire analysis is carried out within the framework of linear theory.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103643"},"PeriodicalIF":2.5,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145332985","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 : 2025-10-09DOI: 10.1016/j.wavemoti.2025.103648
David Kibe Muchiri , Mathieu Sellier , James N. Hewett , Miguel Moyers-González , Jérôme Monnier
A formal comparative numerical study of the lubrication approximation and the shallow water equations (SWE) for three-dimensional Herschel–Bulkley viscoplastic flows is presented. The validity limits and predictive capabilities of these models are compared across various flow regimes, i.e., in terms of the aspect ratio, inclination angle, rheological properties, basal slipperiness, and Reynolds, Froude, and Bingham numbers. The models’ abilities to capture flow deflections around obstructions are also evaluated. For validation, both model solutions are compared to dam-break experiments. In contrast to some previous works in the literature, both models are shown to adequately reproduce the experimental data in the low Reynolds number regime. The key difference arises during the early phase of a dam-break, where local Froude numbers are high, with the lubrication approximation appearing to overestimate front positions, whereas the SWE solutions align more closely with experimental observations. Furthermore, SWE provides better predictions of flow perturbations caused by obstructions and basal slipperiness. Overall, due to the inclusion of inertial effects, the present SWE model demonstrates broader predictive capability for viscoplastic flow dynamics than the lubrication approximation. However, both models converge as the inclination, aspect ratio, local perturbations, Froude and Reynolds numbers decrease, and as the Bingham number increases.
{"title":"Comparing lubrication approximation with shallow water equations for viscoplastic flows","authors":"David Kibe Muchiri , Mathieu Sellier , James N. Hewett , Miguel Moyers-González , Jérôme Monnier","doi":"10.1016/j.wavemoti.2025.103648","DOIUrl":"10.1016/j.wavemoti.2025.103648","url":null,"abstract":"<div><div>A formal comparative numerical study of the lubrication approximation and the shallow water equations (SWE) for three-dimensional Herschel–Bulkley viscoplastic flows is presented. The validity limits and predictive capabilities of these models are compared across various flow regimes, i.e., in terms of the aspect ratio, inclination angle, rheological properties, basal slipperiness, and Reynolds, Froude, and Bingham numbers. The models’ abilities to capture flow deflections around obstructions are also evaluated. For validation, both model solutions are compared to dam-break experiments. In contrast to some previous works in the literature, both models are shown to adequately reproduce the experimental data in the low Reynolds number regime. The key difference arises during the early phase of a dam-break, where local Froude numbers are high, with the lubrication approximation appearing to overestimate front positions, whereas the SWE solutions align more closely with experimental observations. Furthermore, SWE provides better predictions of flow perturbations caused by obstructions and basal slipperiness. Overall, due to the inclusion of inertial effects, the present SWE model demonstrates broader predictive capability for viscoplastic flow dynamics than the lubrication approximation. However, both models converge as the inclination, aspect ratio, local perturbations, Froude and Reynolds numbers decrease, and as the Bingham number increases.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103648"},"PeriodicalIF":2.5,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145332983","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 : 2025-10-08DOI: 10.1016/j.wavemoti.2025.103650
Liru Wang, Zhaqilao
In this paper, we investigate the construction of rogue wave solutions for the (2+1)-dimensional Calogero-Degasperis system on periodic backgrounds. By combining the Jacobian elliptic function expansion method, Darboux transformation techniques, and nonlinearization of the Lax pair, we successfully derive exact rogue wave solutions on the Jacobian elliptic function dn and cn backgrounds. Our analysis reveals important relationships among the three potential functions in the system and demonstrates unique dynamic features of interactions between rogue waves and periodic structures in high-dimensional nonlinear settings.
{"title":"Rogue waves on the periodic background in the (2+1)-dimensional Calogero–Degasperis system","authors":"Liru Wang, Zhaqilao","doi":"10.1016/j.wavemoti.2025.103650","DOIUrl":"10.1016/j.wavemoti.2025.103650","url":null,"abstract":"<div><div>In this paper, we investigate the construction of rogue wave solutions for the (2+1)-dimensional Calogero-Degasperis system on periodic backgrounds. By combining the Jacobian elliptic function expansion method, Darboux transformation techniques, and nonlinearization of the Lax pair, we successfully derive exact rogue wave solutions on the Jacobian elliptic function dn and cn backgrounds. Our analysis reveals important relationships among the three potential functions in the system and demonstrates unique dynamic features of interactions between rogue waves and periodic structures in high-dimensional nonlinear settings.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103650"},"PeriodicalIF":2.5,"publicationDate":"2025-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269626","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 : 2025-10-04DOI: 10.1016/j.wavemoti.2025.103647
Haifang Song, Songlin Zhao, Bo Ren
In this paper, we concentrate on the rogue waves, breathers and hybrid solutions of the coupled Boussinesq system via the Kadomtsev–Petviashvili (KP) hierarchy reduction method. We construct the Gram determinant solutions for a -dimensional bilinear system in the KP hierarchy which can be reduced to the coupled Boussinesq system. By considering the dimension-reduction condition, the general high-order rogue wave solutions expressed by derivatives with respect to parameters and are derived. For simplicity, the expressions of the rogue waves are replaced by purely algebraic ones with the help of the known Schur polynomials. The rogue waves from first till fourth order and their dynamic properties are numerically investigated. The structures of the th-order rogue waves contain first-order rogue waves. As more free parameters appear, the number of patterns increases. The breather solutions are obtained through setting specific parameter conditions in soliton solutions. Then first- and second-order breathers are attained and their dynamics are analyzed numerically. Three different arrangements for the first-order breathers as well as three types of second-order breather waves including interacting waves, parallel waves and coincident waves are displayed. The hybrid solutions containing first-order breather as well as first- and second-order solitons are given with dynamic analysis. A similar way can be used to obtain the th-order rogue waves and the th-order breathers. The method used in the paper can be extended to other integrable equations theoretically.
{"title":"General rogue waves, breathers and hybrid structures of the coupled Boussinesq system","authors":"Haifang Song, Songlin Zhao, Bo Ren","doi":"10.1016/j.wavemoti.2025.103647","DOIUrl":"10.1016/j.wavemoti.2025.103647","url":null,"abstract":"<div><div>In this paper, we concentrate on the rogue waves, breathers and hybrid solutions of the coupled Boussinesq system via the Kadomtsev–Petviashvili (KP) hierarchy reduction method. We construct the Gram determinant solutions for a <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional bilinear system in the KP hierarchy which can be reduced to the coupled Boussinesq system. By considering the dimension-reduction condition, the general high-order rogue wave solutions expressed by derivatives with respect to parameters <span><math><mi>p</mi></math></span> and <span><math><mi>q</mi></math></span> are derived. For simplicity, the expressions of the rogue waves are replaced by purely algebraic ones with the help of the known Schur polynomials. The rogue waves from first till fourth order and their dynamic properties are numerically investigated. The structures of the <span><math><mi>N</mi></math></span>th-order rogue waves contain <span><math><mfrac><mrow><mi>N</mi><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> first-order rogue waves. As more free parameters appear, the number of patterns increases. The breather solutions are obtained through setting specific parameter conditions in soliton solutions. Then first- and second-order breathers are attained and their dynamics are analyzed numerically. Three different arrangements for the first-order breathers as well as three types of second-order breather waves including interacting waves, parallel waves and coincident waves are displayed. The hybrid solutions containing first-order breather as well as first- and second-order solitons are given with dynamic analysis. A similar way can be used to obtain the <span><math><mi>N</mi></math></span>th-order rogue waves and the <span><math><mi>M</mi></math></span>th-order breathers. The method used in the paper can be extended to other integrable equations theoretically.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103647"},"PeriodicalIF":2.5,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269627","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 : 2025-10-01DOI: 10.1016/j.wavemoti.2025.103646
A. Atteya , Reem Altuijri , Kottakkaran Sooppy Nisar , Abdel-Haleem Abdel-Aty , M. Abd-Elzaher , Pralay Kumar Karmakar
This research explores the higher-order nonlinear and dissipative effects on dust acoustic shock waves in a complex plasma medium composed of inertial negative dust particles, Maxwellian electrons, and superthermal ions under the influence of polarization forces. Employing a perturbative approach, the research derives analytical descriptions of both first- and second-order potentials and electric fields, highlighting how these higher-order corrections significantly modify the shock wave structures. The analysis reveals that second-order potentials introduce negative contributions that reduce the overall wave amplitude, while the associated electric fields oppose the first-order fields, leading to self-regulating mechanisms that influence energy transport and wave stability. Numerical evaluations demonstrate how key plasma parameters, such as polarization strength, dust temperature, ion-to-electron density ratio, viscosity, and superthermality-affect phase velocity, nonlinearity, and shock profiles. The findings emphasize that including higher-order effects is crucial for accurately modeling shock dynamics in laboratory with direct relevance to astrophysical plasmas, notably the dynamics observed in planetary ring systems and cosmic dust environments, providing deeper insight into energy dissipation and wave evolution in complex dusty plasma systems.
{"title":"Elevating plasma physics: The role of higher-order nonlinearities in space dust shock waves with superthermal ions","authors":"A. Atteya , Reem Altuijri , Kottakkaran Sooppy Nisar , Abdel-Haleem Abdel-Aty , M. Abd-Elzaher , Pralay Kumar Karmakar","doi":"10.1016/j.wavemoti.2025.103646","DOIUrl":"10.1016/j.wavemoti.2025.103646","url":null,"abstract":"<div><div>This research explores the higher-order nonlinear and dissipative effects on dust acoustic shock waves in a complex plasma medium composed of inertial negative dust particles, Maxwellian electrons, and superthermal ions under the influence of polarization forces. Employing a perturbative approach, the research derives analytical descriptions of both first- and second-order potentials and electric fields, highlighting how these higher-order corrections significantly modify the shock wave structures. The analysis reveals that second-order potentials introduce negative contributions that reduce the overall wave amplitude, while the associated electric fields oppose the first-order fields, leading to self-regulating mechanisms that influence energy transport and wave stability. Numerical evaluations demonstrate how key plasma parameters, such as polarization strength, dust temperature, ion-to-electron density ratio, viscosity, and superthermality-affect phase velocity, nonlinearity, and shock profiles. The findings emphasize that including higher-order effects is crucial for accurately modeling shock dynamics in laboratory with direct relevance to astrophysical plasmas, notably the dynamics observed in planetary ring systems and cosmic dust environments, providing deeper insight into energy dissipation and wave evolution in complex dusty plasma systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103646"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269628","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 : 2025-09-30DOI: 10.1016/j.wavemoti.2025.103645
P. Negi , T. Sahoo , V. Sriram , Y. Stepanyants
This paper provides a detailed analytic solution for examining the scattering of surface gravity waves by an array of bars. Depending on the incident wave period, bars are modelled as either trapezoidal or hump-shaped profiles. We formulate the problem as a boundary value problem governed by the mild-slope equation and employ the transfer matrix method to determine the scattering coefficients. Our analysis reveals that the number of bars and their spacing modulate Bragg resonance characteristics, with the number of sub-harmonic peaks between harmonic peaks being two fewer than the number of bars. For non-uniform bar arrays, rainbow reflection occurs, suppressing sub-harmonic peaks and eliminating multiple zeros in wave reflection. As the bar length approaches the water depth, wave diffraction becomes significant. Complete wave reflection by uniform bar arrays demonstrates a behaviour analogous to Fabry-Pérot resonance in optics. The Bragg reflection patterns exhibit distinctive properties: common zero minima for even numbers of bars and common maxima for odd numbers. When examining the inverse case — submerged trenches instead of bars — we observe similar harmonic and subharmonic components with consistent phase shifts and notably reduced reflected wave amplitudes. Wave field analysis demonstrates three distinct regions: standing waves on the incident side, progressive waves on the leeward side, and partly standing waves in the confined region between bars. The sloped geometries of the bar systems induce wave refraction and amplitude decay. Two-dimensional linear time-dependent surface elevations, simulated using a Gaussian pulse, capture the transient wave transformation dynamics throughout the submerged multi-bar systems.
{"title":"Wave scattering by an array of submerged bars: An analytic approach","authors":"P. Negi , T. Sahoo , V. Sriram , Y. Stepanyants","doi":"10.1016/j.wavemoti.2025.103645","DOIUrl":"10.1016/j.wavemoti.2025.103645","url":null,"abstract":"<div><div>This paper provides a detailed analytic solution for examining the scattering of surface gravity waves by an array of bars. Depending on the incident wave period, bars are modelled as either trapezoidal or hump-shaped profiles. We formulate the problem as a boundary value problem governed by the mild-slope equation and employ the transfer matrix method to determine the scattering coefficients. Our analysis reveals that the number of bars and their spacing modulate Bragg resonance characteristics, with the number of sub-harmonic peaks between harmonic peaks being two fewer than the number of bars. For non-uniform bar arrays, rainbow reflection occurs, suppressing sub-harmonic peaks and eliminating multiple zeros in wave reflection. As the bar length approaches the water depth, wave diffraction becomes significant. Complete wave reflection by uniform bar arrays demonstrates a behaviour analogous to Fabry-Pérot resonance in optics. The Bragg reflection patterns exhibit distinctive properties: common zero minima for even numbers of bars and common maxima for odd numbers. When examining the inverse case — submerged trenches instead of bars — we observe similar harmonic and subharmonic components with consistent phase shifts and notably reduced reflected wave amplitudes. Wave field analysis demonstrates three distinct regions: standing waves on the incident side, progressive waves on the leeward side, and partly standing waves in the confined region between bars. The sloped geometries of the bar systems induce wave refraction and amplitude decay. Two-dimensional linear time-dependent surface elevations, simulated using a Gaussian pulse, capture the transient wave transformation dynamics throughout the submerged multi-bar systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103645"},"PeriodicalIF":2.5,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227791","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 : 2025-09-27DOI: 10.1016/j.wavemoti.2025.103634
Boyuan Yu
The nonlinear development of roll waves in two-layer gravity currents on mild slopes are numerically investigated using an integrated layer model including inertia effect. Periodic roll waves and roll-wave packets initiated by localized disturbance are examined for a realistic range of density and viscosity ratios. When a localized disturbance is introduced initially, the leading wave in the roll-wave packet for both of the layers (referred to as the ”front runner”) could develop exceedingly large peak depth and velocity which increase as the wave packet travels downstream. The upper-layer roll wave and lower-layer roll wave show different characteristics. The amplitude of upper-layer roll wave was found to be significantly larger than that of the lower-layer roll wave. Furthermore, peaks of upper-layer periodic roll waves or front runners always coincide with the shock-like wavefront, while peaks of lower-layer front runners with sufficiently large amplitudes are connected to the shock-like wavefront by a smooth profile. Simulations for three-dimensional two-layer flows using the integrated layer model extended to two dimensions demonstrate similar front-runner existence. However, the three-dimensional front runner has remarkably smaller peak depth and velocity than its unidirectional counterpart due to the transversal spreading of the wavefront.
{"title":"Two-layer roll waves in rapid gravity currents on mild slopes","authors":"Boyuan Yu","doi":"10.1016/j.wavemoti.2025.103634","DOIUrl":"10.1016/j.wavemoti.2025.103634","url":null,"abstract":"<div><div>The nonlinear development of roll waves in two-layer gravity currents on mild slopes are numerically investigated using an integrated layer model including inertia effect. Periodic roll waves and roll-wave packets initiated by localized disturbance are examined for a realistic range of density and viscosity ratios. When a localized disturbance is introduced initially, the leading wave in the roll-wave packet for both of the layers (referred to as the ”front runner”) could develop exceedingly large peak depth and velocity which increase as the wave packet travels downstream. The upper-layer roll wave and lower-layer roll wave show different characteristics. The amplitude of upper-layer roll wave was found to be significantly larger than that of the lower-layer roll wave. Furthermore, peaks of upper-layer periodic roll waves or front runners always coincide with the shock-like wavefront, while peaks of lower-layer front runners with sufficiently large amplitudes are connected to the shock-like wavefront by a smooth profile. Simulations for three-dimensional two-layer flows using the integrated layer model extended to two dimensions demonstrate similar front-runner existence. However, the three-dimensional front runner has remarkably smaller peak depth and velocity than its unidirectional counterpart due to the transversal spreading of the wavefront.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103634"},"PeriodicalIF":2.5,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227528","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 : 2025-09-26DOI: 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}
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