Pub Date : 2026-04-15Epub Date: 2026-02-11DOI: 10.1016/j.wavemoti.2026.103721
Haoran Xu , Zhaoyong Sun , Liuxian Zhao , Yi Chen , Jun Yang
This study proposes a pentamode Luneburg cloak (PMLC) based on the principles of transformation acoustics. By converting the traditional Luneburg lens (LL) into a concentric layered structure and employing discretized pentamode unit cells to achieve graded material properties, the PMLC retains omnidirectional focusing capability while enabling both acoustic wave manipulation and cloaking. Numerical simulations demonstrate that the proposed PMLC exhibits effective broadband performance for both focusing and cloaking within the 5 – 15 kHz frequency range. Analysis of the reflection cross-section reveals that the PMLC maintains low reflectivity over a wide frequency band, with performance comparable to cloaks based on continuous transformation. The PMLC not only enables underwater acoustic cloaking but also supports reverse acoustic localization, offering a novel technological solution for applications involving underwater target concealment and acoustic positioning.
{"title":"Luneburg cloak with pentamode metafluid","authors":"Haoran Xu , Zhaoyong Sun , Liuxian Zhao , Yi Chen , Jun Yang","doi":"10.1016/j.wavemoti.2026.103721","DOIUrl":"10.1016/j.wavemoti.2026.103721","url":null,"abstract":"<div><div>This study proposes a pentamode Luneburg cloak (PMLC) based on the principles of transformation acoustics. By converting the traditional Luneburg lens (LL) into a concentric layered structure and employing discretized pentamode unit cells to achieve graded material properties, the PMLC retains omnidirectional focusing capability while enabling both acoustic wave manipulation and cloaking. Numerical simulations demonstrate that the proposed PMLC exhibits effective broadband performance for both focusing and cloaking within the 5 – 15 kHz frequency range. Analysis of the reflection cross-section reveals that the PMLC maintains low reflectivity over a wide frequency band, with performance comparable to cloaks based on continuous transformation. The PMLC not only enables underwater acoustic cloaking but also supports reverse acoustic localization, offering a novel technological solution for applications involving underwater target concealment and acoustic positioning.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103721"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174611","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 : 2026-04-15Epub Date: 2026-02-04DOI: 10.1016/j.wavemoti.2026.103714
Anıl Çelik
The continuous monitoring of ocean waves is vital for maritime safety, coastal engineering, and climate forecasting. However, wave records from offshore buoys are frequently incomplete due to sensor malfunctions, power failures, or extreme weather, resulting in fragmented datasets that hinder long-term analysis. This study proposes a robust framework for recovering these records using compressed sensing, a signal processing technique designed to reconstruct complete datasets from very sparse and fragmented observations. To enhance reconstruction accuracy, hybrid models that first decompose complex wave signals into simpler patterns using mathematical transforms are developed. Specifically, a Fourier-based Compressed Sensing (F-CS) model is introduced, which identifies the underlying periodic trends and seasonal cycles of the ocean (deterministic components) to provide a stable foundation for reconstructing the missing data points. The evaluation of this approach on high-energy stations in the Atlantic and Pacific Oceans demonstrates that the hybrid framework can accurately reconstruct sea states even when only 10 to 30 % of the original data is available. By utilizing stratified sampling to ensure that both calm and extreme storm conditions are represented during testing, the F-CS model is shown to significantly outperform standard reconstruction methods. It captures critical storm peaks and intricate wave fluctuations with high precision. This methodology provides a powerful, self-contained tool for maintaining the integrity of oceanographic databases and ensures that the physical characteristics of extreme events are preserved even in highly sparse datasets.
{"title":"Improving missing data imputation in significant wave height time series data using Fourier-wavelet-based compressed sensing","authors":"Anıl Çelik","doi":"10.1016/j.wavemoti.2026.103714","DOIUrl":"10.1016/j.wavemoti.2026.103714","url":null,"abstract":"<div><div>The continuous monitoring of ocean waves is vital for maritime safety, coastal engineering, and climate forecasting. However, wave records from offshore buoys are frequently incomplete due to sensor malfunctions, power failures, or extreme weather, resulting in fragmented datasets that hinder long-term analysis. This study proposes a robust framework for recovering these records using compressed sensing, a signal processing technique designed to reconstruct complete datasets from very sparse and fragmented observations. To enhance reconstruction accuracy, hybrid models that first decompose complex wave signals into simpler patterns using mathematical transforms are developed. Specifically, a Fourier-based Compressed Sensing (F-CS) model is introduced, which identifies the underlying periodic trends and seasonal cycles of the ocean (deterministic components) to provide a stable foundation for reconstructing the missing data points. The evaluation of this approach on high-energy stations in the Atlantic and Pacific Oceans demonstrates that the hybrid framework can accurately reconstruct sea states even when only 10 to 30 % of the original data is available. By utilizing stratified sampling to ensure that both calm and extreme storm conditions are represented during testing, the F-CS model is shown to significantly outperform standard reconstruction methods. It captures critical storm peaks and intricate wave fluctuations with high precision. This methodology provides a powerful, self-contained tool for maintaining the integrity of oceanographic databases and ensures that the physical characteristics of extreme events are preserved even in highly sparse datasets.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103714"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174612","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 : 2026-04-15Epub Date: 2026-01-27DOI: 10.1016/j.wavemoti.2026.103706
R. Shabani , F. Honarvar
The objective of this paper is to present a mathematical model for the analysis of the propagation of longitudinal ultrasonic waves in thick-walled cylinders during circumferential scanning in the presence of a thermal gradient. In this study, the angle of entry of the wave (incidence angle), the outer radius of the cylinder, and the temperature of the inner surface of the cylinder are identified as independent variables. A closed-form equation is derived for the incidence angle at which the waves become tangent to the internal surface of the cylinder (tangent angle). The results obtained from the theoretical model indicate that the effect of the temperature of the cylinder's inner surface on the velocity and travel-path of ultrasonic waves is significantly greater than that of the other two variables, particularly at incidence angles approaching the tangent angle. Moreover, at lower temperature gradients (300–450 K), the discrepancy between the mean wave velocity () and the wave velocity at mean temperature () is minimal; however, at higher temperature gradients, the discrepancy is more pronounced and cannot be disregarded. Furthermore, measurements were conducted on a test rig to verify the validity of the developed mathematical model at both normal and oblique incidence angles. The experimental results are found to be in good agreement with the developed model.
{"title":"Modelling of the propagation of ultrasonic waves in thick-walled cylinders during circumferential scanning","authors":"R. Shabani , F. Honarvar","doi":"10.1016/j.wavemoti.2026.103706","DOIUrl":"10.1016/j.wavemoti.2026.103706","url":null,"abstract":"<div><div>The objective of this paper is to present a mathematical model for the analysis of the propagation of longitudinal ultrasonic waves in thick-walled cylinders during circumferential scanning in the presence of a thermal gradient. In this study, the angle of entry of the wave (incidence angle), the outer radius of the cylinder, and the temperature of the inner surface of the cylinder are identified as independent variables. A closed-form equation is derived for the incidence angle at which the waves become tangent to the internal surface of the cylinder (tangent angle). The results obtained from the theoretical model indicate that the effect of the temperature of the cylinder's inner surface on the velocity and travel-path of ultrasonic waves is significantly greater than that of the other two variables, particularly at incidence angles approaching the tangent angle. Moreover, at lower temperature gradients (300–450 K), the discrepancy between the mean wave velocity (<span><math><msub><mi>c</mi><mi>γ</mi></msub></math></span>) and the wave velocity at mean temperature (<span><math><msub><mi>c</mi><mi>m</mi></msub></math></span>) is minimal; however, at higher temperature gradients, the discrepancy is more pronounced and cannot be disregarded. Furthermore, measurements were conducted on a test rig to verify the validity of the developed mathematical model at both normal and oblique incidence angles. The experimental results are found to be in good agreement with the developed model.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103706"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174613","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 : 2026-04-15Epub Date: 2026-02-08DOI: 10.1016/j.wavemoti.2026.103716
Jianan Wang, Yi Zhang, Xiangyun Wang, Jiajie Wu
Based on the Riemann-Hilbert approach, we focus on the higher-order soliton solutions and their dynamical properties for the reverse space-time nonlocal real focusing modified Korteweg-de Vries equation. By analyzing the spectral problem and constructing the corresponding Riemann-Hilbert problem, we first derive the N-soliton solutions of the equation. Building on this foundation, the core contribution of this work is the systematic derivation of explicit expressions for higher-order soliton solutions of this equation through the introduction of perturbation parameters and limiting techniques. Analysis shows that these higher-order solutions exhibit richer dynamical behaviors compared to ordinary solitons.
{"title":"General solitons and higher-order solitons of the nonlocal real focusing modified Korteweg-de Vries equation","authors":"Jianan Wang, Yi Zhang, Xiangyun Wang, Jiajie Wu","doi":"10.1016/j.wavemoti.2026.103716","DOIUrl":"10.1016/j.wavemoti.2026.103716","url":null,"abstract":"<div><div>Based on the Riemann-Hilbert approach, we focus on the higher-order soliton solutions and their dynamical properties for the reverse space-time nonlocal real focusing modified Korteweg-de Vries equation. By analyzing the spectral problem and constructing the corresponding Riemann-Hilbert problem, we first derive the <em>N</em>-soliton solutions of the equation. Building on this foundation, the core contribution of this work is the systematic derivation of explicit expressions for higher-order soliton solutions of this equation through the introduction of perturbation parameters and limiting techniques. Analysis shows that these higher-order solutions exhibit richer dynamical behaviors compared to ordinary solitons.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103716"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174609","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 : 2026-04-15Epub Date: 2026-02-11DOI: 10.1016/j.wavemoti.2026.103720
Xueping Cheng , Jianan Wang
Although the principle of linear superposition is fundamentally incompatible with most nonlinear systems, it is surprisingly discovered that certain exceptional nonlinear equations can accommodate such superposition properties. This phenomenon is demonstrated in this article by taking the generalized (2+1)-dimensional KdV equation as a representative instance. The research begins with the derivation of six distinct variable separation systems, which is achieved by imposing precise coefficient constraints to facilitate the separation of variables. Subsequently, the linear superposition solutions within these decomposition systems are systematically investigated, and three typical solution structures are presented. These include the linear superposition solution of one- and two-solitons, hybrid solutions integrating one-soliton and breather, and composite solutions of two-solitons and periodic waves.
{"title":"Linear superposition solutions of the generalized (2+1)-dimensional KdV equation","authors":"Xueping Cheng , Jianan Wang","doi":"10.1016/j.wavemoti.2026.103720","DOIUrl":"10.1016/j.wavemoti.2026.103720","url":null,"abstract":"<div><div>Although the principle of linear superposition is fundamentally incompatible with most nonlinear systems, it is surprisingly discovered that certain exceptional nonlinear equations can accommodate such superposition properties. This phenomenon is demonstrated in this article by taking the generalized (2+1)-dimensional KdV equation as a representative instance. The research begins with the derivation of six distinct variable separation systems, which is achieved by imposing precise coefficient constraints to facilitate the separation of variables. Subsequently, the linear superposition solutions within these decomposition systems are systematically investigated, and three typical solution structures are presented. These include the linear superposition solution of one- and two-solitons, hybrid solutions integrating one-soliton and breather, and composite solutions of two-solitons and periodic waves.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103720"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385581","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 : 2026-04-15Epub Date: 2026-01-22DOI: 10.1016/j.wavemoti.2026.103705
Jiayi Que , Gongyao Chu , Weijian Zhou
As acoustic devices race toward intelligence and miniaturization, the fixed geometry of passive metasurfaces renders them unable to adapt to dynamic environments, underscoring the urgent need for actively tunable counterparts. Here, we propose a piezoelectric membrane metasurface steered by negative-capacitance circuits to shatter the tuning inflexibility of passive metamaterials. A multiphysics model that unites vibro-acoustic and piezoelectric couplings, solved by finite element simulations, elucidates how circuit parameters alone can continuously tailor the effective Young’s modulus and reflection phase across 0–2π without any structural alteration, liberating the design from dimensional constraints. Leveraging this principle, we realize a reconfigurable intelligent metasurface that performs anomalous reflection and planar acoustic focusing, with simulations in excellent agreement with theory. Combining a sub-wavelength footprint, microsecond response and high fidelity, this active-tuning paradigm charts a fresh route for next-generation smart acoustics in noise control and ultrasonic imaging.
{"title":"Active tuning of reflected acoustic wave with piezoelectric membrane metasurfaces","authors":"Jiayi Que , Gongyao Chu , Weijian Zhou","doi":"10.1016/j.wavemoti.2026.103705","DOIUrl":"10.1016/j.wavemoti.2026.103705","url":null,"abstract":"<div><div>As acoustic devices race toward intelligence and miniaturization, the fixed geometry of passive metasurfaces renders them unable to adapt to dynamic environments, underscoring the urgent need for actively tunable counterparts. Here, we propose a piezoelectric membrane metasurface steered by negative-capacitance circuits to shatter the tuning inflexibility of passive metamaterials. A multiphysics model that unites vibro-acoustic and piezoelectric couplings, solved by finite element simulations, elucidates how circuit parameters alone can continuously tailor the effective Young’s modulus and reflection phase across 0–2π without any structural alteration, liberating the design from dimensional constraints. Leveraging this principle, we realize a reconfigurable intelligent metasurface that performs anomalous reflection and planar acoustic focusing, with simulations in excellent agreement with theory. Combining a sub-wavelength footprint, microsecond response and high fidelity, this active-tuning paradigm charts a fresh route for next-generation smart acoustics in noise control and ultrasonic imaging.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103705"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146081324","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}
Effective control of low-frequency broadband noise remains a persistent challenge in the field of modern acoustics engineering. The challenge arises from inherent limitations in balancing structural size, bandwidth and low-frequency performance. To overcome these issues, we propose a synergistic composite sonic black hole metastructure (CSBH). The design organically integrates the sonic black hole, gradient micro-perforated panels and porous materials, enabling synergistic control of sound wave propagation and energy conversion processes. The study establishes a theoretical model based on the transfer matrix method, fabricates samples using a split-type process, and validates the model through finite element simulation and impedance tube experiments. The results demonstrate that the CSBH achieves near-perfect sound absorption (α≥0.9) starting from 307 Hz, with a structural thickness of only 1/11.2 of the corresponding wavelength, while maintaining an average absorption coefficient above 0.9 over the frequency range of 50–3000 Hz. Furthermore, a systematic parametric analysis is conducted to investigate the influence of geometric parameters of sonic black hole and micro-perforated plates, as well as the characteristics of porous materials. The proposed CSBH provides an effective solution for low-frequency broadband noise control, while also establishing a generalized synergistic design framework for advanced acoustic metamaterials.
{"title":"A synergistic composite sonic black hole metastructure for sub-wavelength broadband sound absorption","authors":"Kai-Di Zhang , Jin-Shui Yang , Shi-Jun Chen , Yi-Dan Chen","doi":"10.1016/j.wavemoti.2026.103718","DOIUrl":"10.1016/j.wavemoti.2026.103718","url":null,"abstract":"<div><div>Effective control of low-frequency broadband noise remains a persistent challenge in the field of modern acoustics engineering. The challenge arises from inherent limitations in balancing structural size, bandwidth and low-frequency performance. To overcome these issues, we propose a synergistic composite sonic black hole metastructure (CSBH). The design organically integrates the sonic black hole, gradient micro-perforated panels and porous materials, enabling synergistic control of sound wave propagation and energy conversion processes. The study establishes a theoretical model based on the transfer matrix method, fabricates samples using a split-type process, and validates the model through finite element simulation and impedance tube experiments. The results demonstrate that the CSBH achieves near-perfect sound absorption (<em>α</em>≥0.9) starting from 307 Hz, with a structural thickness of only 1/11.2 of the corresponding wavelength, while maintaining an average absorption coefficient above 0.9 over the frequency range of 50–3000 Hz. Furthermore, a systematic parametric analysis is conducted to investigate the influence of geometric parameters of sonic black hole and micro-perforated plates, as well as the characteristics of porous materials. The proposed CSBH provides an effective solution for low-frequency broadband noise control, while also establishing a generalized synergistic design framework for advanced acoustic metamaterials.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103718"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174614","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 : 2026-04-15Epub Date: 2026-02-05DOI: 10.1016/j.wavemoti.2026.103715
L. De Abreu Corrêa , S. Khazaie , C. Gomez , R. Cottereau
This paper reports a series of numerical experiments comparing solutions of the 3D acoustic wave equation in a (randomly-fluctuating) heterogeneous medium to solutions of the radiative transfer equation. Parameters of the two equations are first chosen such that the radiative transfer solution is expected to provide an accurate approximation of the energy of the wave (weak-coupling regime), and the comparisons are excellent. Further simulations indicate that radiative transfer provides accurate approximations not only in the expected regime, but also for a wide range of frequencies and fluctuation levels of the propagation medium parameters, as long as the background velocity is appropriately selected. A particular attention is devoted to comparing wave solutions and radiative transfer approximations close to boundaries, where the accuracy of the radiative transfer equation has not been evaluated before.
{"title":"Quantitative error assessment of radiative transfer approximations of acoustic wave energies in unbounded and bounded random media","authors":"L. De Abreu Corrêa , S. Khazaie , C. Gomez , R. Cottereau","doi":"10.1016/j.wavemoti.2026.103715","DOIUrl":"10.1016/j.wavemoti.2026.103715","url":null,"abstract":"<div><div>This paper reports a series of numerical experiments comparing solutions of the 3D acoustic wave equation in a (randomly-fluctuating) heterogeneous medium to solutions of the radiative transfer equation. Parameters of the two equations are first chosen such that the radiative transfer solution is expected to provide an accurate approximation of the energy of the wave (weak-coupling regime), and the comparisons are excellent. Further simulations indicate that radiative transfer provides accurate approximations not only in the expected regime, but also for a wide range of frequencies and fluctuation levels of the propagation medium parameters, as long as the background velocity is appropriately selected. A particular attention is devoted to comparing wave solutions and radiative transfer approximations close to boundaries, where the accuracy of the radiative transfer equation has not been evaluated before.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103715"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174615","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 : 2026-04-15Epub Date: 2026-02-04DOI: 10.1016/j.wavemoti.2026.103713
Yanan Wang , Xi-Hu Wu
This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schrödinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this nonlocal equation is rigorously verified by presenting its associated Lax pair and infinitely many conservation laws. Utilizing the Darboux transformation, we systematically construct a diverse range of localized wave solutions on both zero and nonzero backgrounds. These patterns, such as kinks, exponentially decaying solitons, asymmetric rogue waves and their interaction solutions, exhibit novel dynamical behaviors that are not found in the local counterparts. This work not only enriches the family of solutions for the equation, but also highlights the effectiveness of the Darboux transformation in exploring nonlinear wave dynamics in nonlocal systems.
{"title":"Exact solutions of the reverse space-time higher-order modified self-steepening nonlinear Schrödinger equation","authors":"Yanan Wang , Xi-Hu Wu","doi":"10.1016/j.wavemoti.2026.103713","DOIUrl":"10.1016/j.wavemoti.2026.103713","url":null,"abstract":"<div><div>This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schrödinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this nonlocal equation is rigorously verified by presenting its associated Lax pair and infinitely many conservation laws. Utilizing the Darboux transformation, we systematically construct a diverse range of localized wave solutions on both zero and nonzero backgrounds. These patterns, such as kinks, exponentially decaying solitons, asymmetric rogue waves and their interaction solutions, exhibit novel dynamical behaviors that are not found in the local counterparts. This work not only enriches the family of solutions for the equation, but also highlights the effectiveness of the Darboux transformation in exploring nonlinear wave dynamics in nonlocal systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"143 ","pages":"Article 103713"},"PeriodicalIF":2.5,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174616","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 : 2026-03-15Epub Date: 2026-01-14DOI: 10.1016/j.wavemoti.2026.103702
Mario Lázaro , Marc Martí-Sabaté , Richard V. Craster , Vicent Romero-García
We introduce a weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators with an approach employing the Born approximation and far-field asymptotics of the Green’s function to characterize multiple scattering effects in this system. The response of the system to an incident wave is expressed as a power series expansion where each term introduces higher-order scattering components. The behaviour of this series is governed by the spectral properties of a specific matrix dictating the convergence and accuracy of the weak scattering approximation. By decomposing the scattering response into geometric and physical contributions, we establish a condition for weak scattering in terms of these two factors. This formulation provides a systematic framework for assessing the validity of low-order approximations and understanding wave interactions in complex media. Numerical examples illustrate the accuracy of the weak scattering approximation in periodic and random distributions of scatterers, highlighting implications for wave control and metamaterial design.
{"title":"Weak scattering formulation for flexural waves in thin elastic plates with point-like resonators","authors":"Mario Lázaro , Marc Martí-Sabaté , Richard V. Craster , Vicent Romero-García","doi":"10.1016/j.wavemoti.2026.103702","DOIUrl":"10.1016/j.wavemoti.2026.103702","url":null,"abstract":"<div><div>We introduce a weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators with an approach employing the Born approximation and far-field asymptotics of the Green’s function to characterize multiple scattering effects in this system. The response of the system to an incident wave is expressed as a power series expansion where each term introduces higher-order scattering components. The behaviour of this series is governed by the spectral properties of a specific matrix dictating the convergence and accuracy of the weak scattering approximation. By decomposing the scattering response into geometric and physical contributions, we establish a condition for weak scattering in terms of these two factors. This formulation provides a systematic framework for assessing the validity of low-order approximations and understanding wave interactions in complex media. Numerical examples illustrate the accuracy of the weak scattering approximation in periodic and random distributions of scatterers, highlighting implications for wave control and metamaterial design.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"142 ","pages":"Article 103702"},"PeriodicalIF":2.5,"publicationDate":"2026-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146037395","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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