Wave Motion最新文献

{"title":"Novel nonlocal three-component mKdV equations and classification of solutions","authors":"Mengli Tian ,&nbsp;Chunxia Li ,&nbsp;Fei Li ,&nbsp;Yue Li ,&nbsp;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}

{"title":"The soliton solutions for an integrable nonlocal reverse space–time fifth-order nonlinear Schrödinger equation by the inverse scattering transform","authors":"Huanhuan Lu","doi":"10.1016/j.wavemoti.2025.103619","DOIUrl":"10.1016/j.wavemoti.2025.103619","url":null,"abstract":"<div><div>This paper begins by deducing a reverse space–time nonlocal fifth-order nonlinear Schrödinger (NLS) equation, which arises from a simple yet significant symmetry reduction of the corresponding local system. Following this, the determinant form of <span><math><mi>N</mi></math></span> soliton solutions is thoroughly constructed based on established Gelfand–Levitan–Marchenko(GLM) equation. As a typical application, some exact solutions are derived, including one-soliton, two-soliton, and three-soliton solutions. The dynamical properties of these solutions are further explored and visualized through graphical analysis. Moreover, the integrability of the equation is established by presenting an infinite set of conserved densities. It is particularly noteworthy that we also present the expression for the three-soliton solution, which represents an unprecedented achievement in this field.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103619"},"PeriodicalIF":2.5,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858286","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}

{"title":"Agent-Physics-Informed Neural Network solving frequency-domain Helmholtz equation related forward and inverse problems","authors":"Zeyuan Dong,&nbsp;Chang Su,&nbsp;Hao Chen,&nbsp;Weijun Lin,&nbsp;Yubing Li","doi":"10.1016/j.wavemoti.2025.103580","DOIUrl":"10.1016/j.wavemoti.2025.103580","url":null,"abstract":"<div><div>Accurately solving high-fidelity acoustic fields is critical for advancing ultrasonic research. While conventional numerical solvers remain widely used, emerging approaches like Physics-Informed Neural Networks (PINNs) provide a promising alternative for modeling physical phenomena governed by partial differential equations. However, PINNs often struggle to resolve wavefields in large-scale, complex velocity models described by the Helmholtz equation, limiting their practical applications. To address these issues, we propose the Agent-Physics-Informed Neural Network (APINNs) architecture, which integrates the agent field concept and employs a multi-frequency band training strategy. Initially, APINNs are trained on single-frequency forward problems, with agent fields enhancing sensitivity to scattered waves. Subsequently, a step-by-step training methodology enables APINNs to directly predict scattered wavefields at arbitrary frequencies within a prescribed frequency band. By convolving the scattered fields with the source wavelet and applying an inverse Fourier transform, the time-evolving wave propagation in large-scale, heterogeneous models can also be reconstructed. Moreover, we extend APINNs to imaging-related inverse problems, such as velocity model reconstruction, within an ultrasound computed tomography framework. This extension only requires computational costs less than one order of magnitude higher than forward APINNs. Conversely, conventional FWI shows a higher cost ratio between inverse and forward problems. While this does not mean that inverse APINNs are currently more efficient than traditional FWI — since the ratio reflects only internal balance and forward APINN training remains expensive — training-driven APINNs are better positioned to benefit from advances in deep learning, potentially improving efficiency and scalability. Numerical experiments validate the effectiveness of APINNs in solving both forward and inverse problems based on the Helmholtz equation in complex scenarios.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103580"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241581","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}

{"title":"Proposal of reduced wave vector set approximation model of turbulence due to Shell Model","authors":"Sin-ichi Inage ,&nbsp;Hayato Mizuguchi ,&nbsp;Shoki Oogi","doi":"10.1016/j.wavemoti.2025.103578","DOIUrl":"10.1016/j.wavemoti.2025.103578","url":null,"abstract":"<div><div>Turbulence remains a fundamental challenge in fluid dynamics, with direct numerical simulations (DNS) offering crucial insights at a high computational cost. To bridge the gap between DNS and reduced-order models, we propose the reduced wave-vector set approximation model, an extension of the GOY shell model into three dimensions. This model successfully reproduces key statistical features of homogeneous isotropic turbulence, including the Kolmogorov -5/3 power-law and velocity probability density functions (PDFs) consistent with DNS. However, it fails to capture the asymmetry in the streamwise velocity gradient (∂u/∂x), highlighting the need for anisotropic energy transfer mechanisms. Despite this limitation, our framework presents a computationally efficient approach to turbulence modeling, paving the way for further refinements and broader applications in theoretical and applied sciences.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103578"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146862","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}

{"title":"Pfaffian solution for dark–dark soliton to the coupled complex modified Korteweg–de Vries equation","authors":"Chenxi Li ,&nbsp;Xiaochuan Liu ,&nbsp;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":"2025-11-01","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}

{"title":"Spiral waves and localized modes in dispersive wave equations","authors":"Mark J. Ablowitz ,&nbsp;Justin T. Cole ,&nbsp;Sean D. Nixon","doi":"10.1016/j.wavemoti.2025.103579","DOIUrl":"10.1016/j.wavemoti.2025.103579","url":null,"abstract":"<div><div>Spiral wave patterns are investigated in continuous linear and nonlinear dispersive wave equations. These models can be derived from reductions of lattice Floquet topological insulators. Specifically, continuous nonlinear Dirac and Lieb systems are analyzed. In the linear limit, both of these systems reduce to the Klein–Gordon equation. A stationary phase approximation is used to reveal the structure of the spirals. The spiral solutions of the underlying Klein–Gordon equation explain the dynamics in the motivating Floquet lattice system. In the nonlinear Dirac equation, a family of localized modes in the spectral band gap are found to approach a single low energy pulse. Spiral waves are found in the nonlinear Klein–Gordon equation even with large nonlinear coefficients.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103579"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146863","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}

{"title":"Comprehensive modeling of elastic wave propagation in porous viscoelastic media incorporating fractional-order derivative under welded and loose boundary conditions","authors":"Lijuan Chu ,&nbsp;Li Li ,&nbsp;Yang Liu","doi":"10.1016/j.wavemoti.2025.103609","DOIUrl":"10.1016/j.wavemoti.2025.103609","url":null,"abstract":"<div><div>The complexity and diversity of Earth materials pose significant challenges to seismic detection techniques, especially in oil and gas exploration. The development and application of the viscoelastic theory and microscopic flow theory of porous fluids have made the analysis of elastic wave propagation information one of the main methods of detection. This study investigates the propagation characteristics of elastic waves in a sandwich structure, which comprises of layers of elastic, porous viscoelastic and viscoelastic solids, placed on top of each other. The fractional order Zener model, Biot-squirt flow (BISQ) model, and non-Newtonian fluid theory are employed to describe the viscoelasticity of the solid frame, microscopic flow of porous fluids, and viscosity of porous fluids, respectively. To our knowledge, existing studies on unwelded bonded boundary conditions have not yet incorporated the BISQ model and fractional derivative theory. We aim to address this critical knowledge gap. Both welded and loose boundary conditions have been taken into account in our model. Graphical representations illustrate the numerical simulation findings. Our study suggests that the viscoelasticity of solid frame, the flow characteristics of porous fluids, welded and loose boundary condition have significant impact on the propagation properties of elastic waves. Hence, the study of the above factors in Earth materials will appropriately describe the subsequent dissipation of seismic wave energy and the analysis of stratigraphic structures and soil properties.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103609"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654791","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}

{"title":"Laboratory and numerical experiments of wave propagation in media with fluid-filled fractures","authors":"Ana L. Ramos-Barreto ,&nbsp;Tobias M. Müller ,&nbsp;Rubén Rioyos-Romero ,&nbsp;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":"2025-11-01","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}

{"title":"Perturbation solution for second-harmonic generation in focused shear wave beams in soft solids","authors":"Philip G. Kaufinger ,&nbsp;John M. Cormack ,&nbsp;Kyle S. Spratt ,&nbsp;Mark F. Hamilton","doi":"10.1016/j.wavemoti.2025.103595","DOIUrl":"10.1016/j.wavemoti.2025.103595","url":null,"abstract":"<div><div>Plane nonlinear shear waves in isotropic media are subject only to cubic nonlinearity at leading order and therefore generate only odd harmonics during propagation. Wavefront curvature in shear wave beams breaks the symmetry in the material response and yields quadratic nonlinearity, such that a second harmonic may be generated at second order in a shear wave beam depending on the polarization of the wave field. The governing paraxial wave equation accounting for both quadratic and cubic nonlinearity in isotropic elastic media was derived originally by Zabolotskaya (1986), with its formulation employed in the present work developed subsequently by Wochner et al. (2008). Closed-form analytical solutions for the fields at the source frequency and the second harmonic are derived by perturbation for both the transverse and longitudinal particle displacement components in focused shear wave beams radiated by a source defined by affine polarization, Gaussian amplitude shading, and quadratic phase shading to account for focusing. Examples of field distributions are presented based on parameters reported by Cormack et al. (2024) for measurements of radially polarized focused shear wave beams generated in tissue-mimicking phantoms. Second-harmonic generation in shear wave beams with other polarizations is also discussed. Calculations are presented to estimate the vibration amplitude required for observable second-harmonic generation in tissue-mimicking phantoms. It is postulated that the second harmonic may be used to estimate the third-order elastic material property as an additional biomarker for diseased tissue.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"139 ","pages":"Article 103595"},"PeriodicalIF":2.1,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144471744","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}

{"title":"N-soliton solutions of four-wave mixing coupled Schrödinger equations based on Riemann–Hilbert method","authors":"Xin Wang,&nbsp;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":"2025-11-01","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}