Pub Date : 2025-11-01Epub Date: 2025-07-19DOI: 10.1016/j.wavemoti.2025.103604
Yi-Lin Tian , Wen-Yuan Li , Nong-Sen Li , Rui-Gang Zhang , Ji-Feng Cui
In the text, we deliberate the (3+1)-dimensional variable-coefficient potential Yu-Toda-Sasa-Fukuyama equation (YTST) in an elastic (or in a two-layer-liquid) medium, and its bilinear form is derived by Bell polynomials. Via symbolic computation method and Hirota bilinear form, the first-order, second-order and third-order rogue wave solutions are presented, involving lump-type, lump-kink-type, periodic and line rogue waves. The effect of variable coefficient functions and parameter values of the center on the shapes and peak numbers of rogue waves is demonstrated and explained in terms of three-dimensional graphs and contours. The appearances bearing fission and propagation in the periodic background are duly traced. The novel outcomes fill the gap in rogue wave solutions for this model, which furnish great awareness going deeply into variable coefficient equations.
{"title":"Dynamics of multiple rogue waves for (3+1)-dimensional variable-coefficient potential Yu-Toda-Sasa-Fukuyama equation","authors":"Yi-Lin Tian , Wen-Yuan Li , Nong-Sen Li , Rui-Gang Zhang , Ji-Feng Cui","doi":"10.1016/j.wavemoti.2025.103604","DOIUrl":"10.1016/j.wavemoti.2025.103604","url":null,"abstract":"<div><div>In the text, we deliberate the (3+1)-dimensional variable-coefficient potential Yu-Toda-Sasa-Fukuyama equation (YTST) in an elastic (or in a two-layer-liquid) medium, and its bilinear form is derived by Bell polynomials. Via symbolic computation method and Hirota bilinear form, the first-order, second-order and third-order rogue wave solutions are presented, involving lump-type, lump-kink-type, periodic and line rogue waves. The effect of variable coefficient functions and parameter values of the center on the shapes and peak numbers of rogue waves is demonstrated and explained in terms of three-dimensional graphs and contours. The appearances bearing fission and propagation in the periodic background are duly traced. The novel outcomes fill the gap in rogue wave solutions for this model, which furnish great awareness going deeply into variable coefficient equations.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103604"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686110","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 : 2025-11-01Epub Date: 2025-07-30DOI: 10.1016/j.wavemoti.2025.103615
Bahman Ansari, Alireza Firoozfar
In this study, a time domain boundary-finite element method is developed for solving wave propagation problems. By applying the weighted residual approach and using the static fundamental solutions as the weight function, the wave propagation equation is converted to simple boundary integral. In addition, the effects of domain integral related to inertia term are considered by applying the finite element method to the solution. Furthermore, after deriving the boundary-finite element (Hybrid) formulations, the solvable matrix of the equations in the discretized form is presented. In a novel approach, by estimating the temporal variations of the element nodes using Taylor and Fourier series, a time series discrete matrix is introduced for solving the equations which provides a higher degree of accuracy in compare to other time discretization approaches. Finally, the formulations and method are implemented into a computer algorithm and various examples are solved. The results demonstrated that the proposed time series hybrid approach (TSHEM) accurately models wave propagation problems with lower computational cost in compare to other numerical solutions, making it a preferable choice for solving complex problems with higher accuracy.
{"title":"Wave propagation model by time series hybrid element method","authors":"Bahman Ansari, Alireza Firoozfar","doi":"10.1016/j.wavemoti.2025.103615","DOIUrl":"10.1016/j.wavemoti.2025.103615","url":null,"abstract":"<div><div>In this study, a time domain boundary-finite element method is developed for solving wave propagation problems. By applying the weighted residual approach and using the static fundamental solutions as the weight function, the wave propagation equation is converted to simple boundary integral. In addition, the effects of domain integral related to inertia term are considered by applying the finite element method to the solution. Furthermore, after deriving the boundary-finite element (Hybrid) formulations, the solvable matrix of the equations in the discretized form is presented. In a novel approach, by estimating the temporal variations of the element nodes using Taylor and Fourier series, a time series discrete matrix is introduced for solving the equations which provides a higher degree of accuracy in compare to other time discretization approaches. Finally, the formulations and method are implemented into a computer algorithm and various examples are solved. The results demonstrated that the proposed time series hybrid approach (TSHEM) accurately models wave propagation problems with lower computational cost in compare to other numerical solutions, making it a preferable choice for solving complex problems with higher accuracy.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103615"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757328","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 : 2025-11-01Epub Date: 2025-07-29DOI: 10.1016/j.wavemoti.2025.103612
Muhammad Shoaib , Zhijing Wu , Jiping Jing , Fengming Li , Long Liu
In this paper, the transverse and longitudinal wave motions of a fluid-conveying deployable meta-pipe incorporating periodic inertial amplification (IA) mechanisms are systematically investigated. The proposed structure aims to enhance vibration attenuation based on the band gap (BG) property in low-frequency ranges. The dynamic model of the IA mechanism is established to precisely characterize the inertial forces generated by the coupled axial-bending deformation in the base pipe structure. Based on the Bloch theorem, the dispersion curves are analyzed using the transfer matrix method (TMM). An experiment prototype is manufactured and subjected to vibration testing for validation of the theoretical model. Parametric analysis reveals that both the position and bandwidth of transverse and longitudinal BGs exhibit significant dependence on variations in: (1) fluid velocity, (2) deploying velocity, (3) IA mechanism’s parameters (mass and angle) and (4) the length of the unit cell. This research can establish both theoretical and experimental foundations for engineering design focused on enhanced vibration attenuation in conveying-fluid pipes.
{"title":"Band-gap properties of fluid-conveying deployable meta-pipes with periodic inertial amplification mechanisms","authors":"Muhammad Shoaib , Zhijing Wu , Jiping Jing , Fengming Li , Long Liu","doi":"10.1016/j.wavemoti.2025.103612","DOIUrl":"10.1016/j.wavemoti.2025.103612","url":null,"abstract":"<div><div>In this paper, the transverse and longitudinal wave motions of a fluid-conveying deployable meta-pipe incorporating periodic inertial amplification (IA) mechanisms are systematically investigated. The proposed structure aims to enhance vibration attenuation based on the band gap (BG) property in low-frequency ranges. The dynamic model of the IA mechanism is established to precisely characterize the inertial forces generated by the coupled axial-bending deformation in the base pipe structure. Based on the Bloch theorem, the dispersion curves are analyzed using the transfer matrix method (TMM). An experiment prototype is manufactured and subjected to vibration testing for validation of the theoretical model. Parametric analysis reveals that both the position and bandwidth of transverse and longitudinal BGs exhibit significant dependence on variations in: (1) fluid velocity, (2) deploying velocity, (3) IA mechanism’s parameters (mass and angle) and (4) the length of the unit cell. This research can establish both theoretical and experimental foundations for engineering design focused on enhanced vibration attenuation in conveying-fluid pipes.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103612"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757329","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 : 2025-11-01Epub Date: 2025-07-11DOI: 10.1016/j.wavemoti.2025.103603
Philip Rosenau , Alexander Oron
We introduce and study a class of equations that merge the Gardner’s-type, non-convex, advection with regularized long-wave dispersion, also known as Benjamin–Bona–Mahony equation, to the effect that unlike the unidirectional Gardner solitons, the presented model supports bidirectional propagation of at least three types of solitary waves and begets a whole gallery of chase and collision interactions. Among the novel features of our model, we mention the possibility that one of the solitons reverses its direction upon interaction with another soliton. Extension of the model to higher dimensions typically causes the newly found solitary waves to split into a countable sequence of multi-modal solitary waves wherein either mode’s amplitude increases with its modality, or the modes condense near their potential’s top.
{"title":"Novel solitary patterns in a class of regularized Gardner equations","authors":"Philip Rosenau , Alexander Oron","doi":"10.1016/j.wavemoti.2025.103603","DOIUrl":"10.1016/j.wavemoti.2025.103603","url":null,"abstract":"<div><div>We introduce and study a class of equations that merge the Gardner’s-type, non-convex, advection with regularized long-wave dispersion, also known as Benjamin–Bona–Mahony equation, to the effect that unlike the unidirectional Gardner solitons, the presented model supports bidirectional propagation of at least three types of solitary waves and begets a whole gallery of chase and collision interactions. Among the novel features of our model, we mention the possibility that one of the solitons <em>reverses its direction</em> upon interaction with another soliton. Extension of the model to higher dimensions typically causes the newly found solitary waves to split into <em>a countable sequence of multi-modal solitary waves</em> wherein either mode’s amplitude increases with its modality, or the modes condense near their potential’s top.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103603"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632660","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 : 2025-11-01Epub Date: 2025-06-11DOI: 10.1016/j.wavemoti.2025.103584
Majid Madadi , Mustafa Inc , Mustafa Bayram
Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores a newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev–Petviashvili (KPE) and Boiti–Leon–Manna–Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that it does not satisfy the Painlevé property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.
在现实世界中的应用研究已经推动了非线性科学的进步，流体动力学和等离子体物理学目前引起了极大的关注。结合Kadomtsev-Petviashvili （KPE）和boi - leon - manna - pempinelli （BLMPE）方程，提出了一种新的（2+1）维非线性波动方程。该方程包含非线性和色散项，在流体动力学、等离子体物理、非线性光学和地球物理流中具有潜在的应用。我们分析了它的可积性，表明它不满足painlevel性质，但允许多孤子解。利用Hirota双线性方法和扩展同斜检验方法，我们导出了块波、孤子相互作用和呼吸波等解析解，后者导致异常波的形成。
{"title":"Nonlinear wave behaviors for a combined Kadomtsev–Petviashvili–Boiti–Leon–Manna–Pempinelli equation in fluid dynamics, plasma physics and nonlinear optics","authors":"Majid Madadi , Mustafa Inc , Mustafa Bayram","doi":"10.1016/j.wavemoti.2025.103584","DOIUrl":"10.1016/j.wavemoti.2025.103584","url":null,"abstract":"<div><div>Research in real-world applications has been driving the progress of nonlinear science, with fluid dynamics and plasma physics currently capturing significant attention. This paper explores a newly proposed (2+1)-dimensional nonlinear wave equation, combining the Kadomtsev–Petviashvili (KPE) and Boiti–Leon–Manna–Pempinelli equations (BLMPE). The equation, which includes nonlinear and dispersive terms, has potential applications in fluid dynamics, plasma physics, nonlinear optics, and geophysical flows. We analyze its integrability, showing that it does not satisfy the Painlevé property but admits multi-soliton solutions. Using the Hirota bilinear approach and extended homoclinic test approach, we derive analytic solutions such as lump waves, soliton interactions, and breather waves, with the latter leading to rogue wave formation.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103584"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144281034","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 : 2025-11-01Epub Date: 2025-07-19DOI: 10.1016/j.wavemoti.2025.103606
Elie Salemeh, Simon Félix, Vincent Pagneux
In wave transport through complex media, the single-channel regime is characterized by the loss of sensitivity to incidence conditions, resulting in an invariant pattern of the transmitted wave. So far, such “frozen” patterns have been observed in localized disordered media and in periodic waveguides. In this paper, we show that the same mechanism can occur in the transmission through gratings when properly designed, allowing the observation of the freezing when an incident plane wave is scattered by a grating composed of two successive arrays of scatterers: one mixing the incident orders in arbitrary ways, followed by a freezing array periodically structured in the longitudinal direction, normal to the grating plane. Unlike localized disordered media, where freezing occurs only with evanescent waves, gratings, similarly to periodic waveguides, can exhibit freezing with propagating waves when a single Bloch mode is propagating in the longitudinal direction. Moreover, we show different classes of grating geometries for which the occurrence of freezing is sensitive or insensitive to the incidence angle.
{"title":"Freezing of the transmitted wave pattern through gratings","authors":"Elie Salemeh, Simon Félix, Vincent Pagneux","doi":"10.1016/j.wavemoti.2025.103606","DOIUrl":"10.1016/j.wavemoti.2025.103606","url":null,"abstract":"<div><div>In wave transport through complex media, the single-channel regime is characterized by the loss of sensitivity to incidence conditions, resulting in an invariant pattern of the transmitted wave. So far, such “frozen” patterns have been observed in localized disordered media and in periodic waveguides. In this paper, we show that the same mechanism can occur in the transmission through gratings when properly designed, allowing the observation of the freezing when an incident plane wave is scattered by a grating composed of two successive arrays of scatterers: one mixing the incident orders in arbitrary ways, followed by a freezing array periodically structured in the longitudinal direction, normal to the grating plane. Unlike localized disordered media, where freezing occurs only with evanescent waves, gratings, similarly to periodic waveguides, can exhibit freezing with propagating waves when a single Bloch mode is propagating in the longitudinal direction. Moreover, we show different classes of grating geometries for which the occurrence of freezing is sensitive or insensitive to the incidence angle.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103606"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144714095","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}
Rayleigh waves are prevalent in the ambient seismic noise wavefield and are thus often exploited in passive seismic methods to characterise the near subsurface. In fractured or faulted media, Rayleigh waves show anisotropic velocities that could provide information on the fault properties. However, the exact relationship between Rayleigh wave anisotropy and true anisotropic structures is not well known. This study used a three-component (3C) beamforming toolbox to analyse numerical full waveform seismic wave propagation from conceptual models of fractured media, which depict the nonlinear physical behaviour of the wave. We identify Rayleigh waves in the synthetic data produced from a single point source at different locations, compare observed Rayleigh wave anisotropy to structural anisotropy, and assess the effect array design and source distance have on Rayleigh wave analysis and observed anisotropy. Numerical analysis shows that the smaller the velocity contrast between fault and surrounding rock, the more complex the anisotropic response. We find that the slow directions of Rayleigh wave propagation can be a better indicator of fault strike than the fastest direction, when the velocity contrast between the two media is small.
{"title":"Investigating Rayleigh wave anisotropy in faulted media with three-component beamforming: Insights from numerical models and applications for geothermal exploration","authors":"Heather Kennedy , Claudia Finger , Katrin Löer , Amy Gilligan","doi":"10.1016/j.wavemoti.2025.103596","DOIUrl":"10.1016/j.wavemoti.2025.103596","url":null,"abstract":"<div><div>Rayleigh waves are prevalent in the ambient seismic noise wavefield and are thus often exploited in passive seismic methods to characterise the near subsurface. In fractured or faulted media, Rayleigh waves show anisotropic velocities that could provide information on the fault properties. However, the exact relationship between Rayleigh wave anisotropy and true anisotropic structures is not well known. This study used a three-component (3C) beamforming toolbox to analyse numerical full waveform seismic wave propagation from conceptual models of fractured media, which depict the nonlinear physical behaviour of the wave. We identify Rayleigh waves in the synthetic data produced from a single point source at different locations, compare observed Rayleigh wave anisotropy to structural anisotropy, and assess the effect array design and source distance have on Rayleigh wave analysis and observed anisotropy. Numerical analysis shows that the smaller the velocity contrast between fault and surrounding rock, the more complex the anisotropic response. We find that the slow directions of Rayleigh wave propagation can be a better indicator of fault strike than the fastest direction, when the velocity contrast between the two media is small.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103596"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144510979","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 : 2025-11-01Epub Date: 2025-06-23DOI: 10.1016/j.wavemoti.2025.103601
Majdi O. Gzal , Lawrence A. Bergman , Kathryn H. Matlack , Alexander F. Vakakis
Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve broadband low-frequency sound manipulation at the sub-wavelength scale in a multilayered vibroacoustic metamaterial. Remarkably, we unveil the formation of genuinely sub-wavelength Bragg-like band-splitting induced bandgaps, generalizing the "band-folding induced bandgaps" in the literature. Additionally, we propose a methodology to widen sub-wavelength local resonance bandgaps by hosting two local resonances within the same bandgap. These sub-Bragg phenomena are realized at low frequencies in an axisymmetric vibroacoustic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The coupled sound-structure interaction is solved exactly. The studied system exhibits sub-wavelength acoustical transparency, akin to “electromagnetically induced transparency”, and an acoustic analogue of "plasma oscillations". We derive canonical conditions for the emergence of band-splitting bandgaps, showing they are exclusive to multilayered configurations. These band-splitting bandgaps resemble Bragg bandgaps in their attenuation, band-crossing capabilities, and potential to host topological interface states. We also reveal that classical geometric Bragg diffraction does not apply to the periodic multilayered vibroacoustic configurations examined. The studied sub-wavelength phenomena unlock new possibilities for controlling low-frequency wave propagation in the sub-Bragg regime. Design guidelines for maximizing bandgap width within the low-frequency regime are provided, and the attenuation performance across different bandgaps is demonstrated through numerical simulations. We anticipate that our findings, while demonstrated here in vibroacoustic metamaterials, provide a promising approach for advanced acoustic devices, and could inspire future work exploring similar sub-wavelength mechanisms in other classes of physical systems.
{"title":"Low-frequency sub-Bragg phenomena in multilayered vibroacoustic metamaterials","authors":"Majdi O. Gzal , Lawrence A. Bergman , Kathryn H. Matlack , Alexander F. Vakakis","doi":"10.1016/j.wavemoti.2025.103601","DOIUrl":"10.1016/j.wavemoti.2025.103601","url":null,"abstract":"<div><div>Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve broadband low-frequency sound manipulation at the sub-wavelength scale in a multilayered vibroacoustic metamaterial. Remarkably, we unveil the formation of genuinely sub-wavelength Bragg-like band-splitting induced bandgaps, generalizing the \"band-folding induced bandgaps\" in the literature. Additionally, we propose a methodology to widen sub-wavelength local resonance bandgaps by hosting two local resonances within the same bandgap. These sub-Bragg phenomena are realized at low frequencies in an axisymmetric vibroacoustic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The coupled sound-structure interaction is solved exactly. The studied system exhibits sub-wavelength acoustical transparency, akin to “electromagnetically induced transparency”, and an acoustic analogue of \"plasma oscillations\". We derive canonical conditions for the emergence of band-splitting bandgaps, showing they are exclusive to multilayered configurations. These band-splitting bandgaps resemble Bragg bandgaps in their attenuation, band-crossing capabilities, and potential to host topological interface states. We also reveal that classical geometric Bragg diffraction does not apply to the periodic multilayered vibroacoustic configurations examined. The studied sub-wavelength phenomena unlock new possibilities for controlling low-frequency wave propagation in the sub-Bragg regime. Design guidelines for maximizing bandgap width within the low-frequency regime are provided, and the attenuation performance across different bandgaps is demonstrated through numerical simulations. We anticipate that our findings, while demonstrated here in vibroacoustic metamaterials, provide a promising approach for advanced acoustic devices, and could inspire future work exploring similar sub-wavelength mechanisms in other classes of physical systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103601"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557384","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 : 2025-11-01Epub Date: 2025-08-22DOI: 10.1016/j.wavemoti.2025.103624
Majid Madadi , Mustafa Inc
We derive and characterize general rogue wave solutions (RWSs) of the (3+1)-dimensional Painlevé-type (P-type) integrable nonlinear evolution equation using the Hirota bilinear method in conjunction with the Kadomtsev–Petviashvili hierarchy reduction method (KPHRM). These solutions arise from intricate nonlinear interactions and exhibit diverse dynamical patterns, such as bright and dark triangular, pentagonal, and other structures, governed by key free parameters and the signs of system coefficients. Additionally, we address new nonlinear soliton solutions using the KPHRM in a determinantal framework. To further generalize the model, we incorporate spatiotemporal coefficients, which introduce additional nonlinear modulation. Using the Wronskian approach, another determinant-based technique, we construct -soliton solutions for the variable-coefficient equation and analyze their nonlinear dynamics, demonstrating how parameter variation influences wave evolution and interactions.
{"title":"Determinantal solutions to the (3+1)-dimensional Painlevé-type evolution equation: Higher-order rogue and soliton waves","authors":"Majid Madadi , Mustafa Inc","doi":"10.1016/j.wavemoti.2025.103624","DOIUrl":"10.1016/j.wavemoti.2025.103624","url":null,"abstract":"<div><div>We derive and characterize general rogue wave solutions (RWSs) of the (3+1)-dimensional Painlevé-type (P-type) integrable nonlinear evolution equation using the Hirota bilinear method in conjunction with the Kadomtsev–Petviashvili hierarchy reduction method (KPHRM). These solutions arise from intricate nonlinear interactions and exhibit diverse dynamical patterns, such as bright and dark triangular, pentagonal, and other structures, governed by key free parameters and the signs of system coefficients. Additionally, we address new nonlinear soliton solutions using the KPHRM in a determinantal framework. To further generalize the model, we incorporate spatiotemporal coefficients, which introduce additional nonlinear modulation. Using the Wronskian approach, another determinant-based technique, we construct <span><math><mi>N</mi></math></span>-soliton solutions for the variable-coefficient equation and analyze their nonlinear dynamics, demonstrating how parameter variation influences wave evolution and interactions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103624"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904573","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 : 2025-11-01Epub Date: 2025-08-09DOI: 10.1016/j.wavemoti.2025.103616
Mengli Tian , Chunxia Li , Fei Li , Yue Li , Yuqin Yao
A kind of nonlocal reduction for the unreduced modified Korteweg–de Vries (mKdV) system is presented, which yields the reverse space–time nonlocal complex three-component mKdV (NCTC-mKdV) equation. This equation can be regarded as a new member of the Ablowitz–Kaup–Newell–Segur (AKNS) integrable hierarchy. We develop the Cauchy matrix approach to investigate the solution structure of the nonlocal system systematically, where the Sylvester equation is pivotal in constructing explicit solutions. In fact, the analytical expressions of the solutions can be classified according to the eigenvalue structure of the coefficient matrix in the Sylvester equation. Specially, various explicit solutions of the NCTC-mKdV equation are derived, including soliton solution, Jordan solution and diagonal-Jordan-block mixed solution. Notably, the conditions for generating one-soliton solution, two-soliton solution, mixed solution, periodic solution, double-periodic solution, quasi-periodic solution and dark soliton solution are presented and their dynamic behaviors are analyzed. The results reveal the structural features of solutions to the three-component mKdV equation under nonlocal reduction.
{"title":"Novel nonlocal three-component mKdV equations and classification of solutions","authors":"Mengli Tian , Chunxia Li , Fei Li , Yue Li , Yuqin Yao","doi":"10.1016/j.wavemoti.2025.103616","DOIUrl":"10.1016/j.wavemoti.2025.103616","url":null,"abstract":"<div><div>A kind of nonlocal reduction for the unreduced modified Korteweg–de Vries (mKdV) system is presented, which yields the reverse space–time nonlocal complex three-component mKdV (NCTC-mKdV) equation. This equation can be regarded as a new member of the Ablowitz–Kaup–Newell–Segur (AKNS) integrable hierarchy. We develop the Cauchy matrix approach to investigate the solution structure of the nonlocal system systematically, where the Sylvester equation is pivotal in constructing explicit solutions. In fact, the analytical expressions of the solutions can be classified according to the eigenvalue structure of the coefficient matrix <span><math><mi>K</mi></math></span> in the Sylvester equation. Specially, various explicit solutions of the NCTC-mKdV equation are derived, including soliton solution, Jordan solution and diagonal-Jordan-block mixed solution. Notably, the conditions for generating one-soliton solution, two-soliton solution, mixed solution, periodic solution, double-periodic solution, quasi-periodic solution and dark soliton solution are presented and their dynamic behaviors are analyzed. The results reveal the structural features of solutions to the three-component mKdV equation under nonlocal reduction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103616"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831306","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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