Pub Date : 2024-10-24DOI: 10.1016/j.wavemoti.2024.103425
Xiaodong Liu , Jiguang Sun , Lei Zhang
We propose a computation method for scattering poles of impedance obstacles. Boundary integral equations are used to formulate the problem. It is shown that the scattering poles are the eigenvalues of some integral operator. Then we employ the Nyström method to discretize the integral operator and obtain a nonlinear matrix eigenvalue problem. The eigenvalues are computed using a multistep parallel spectral indicator method. Numerical examples demonstrate the high accuracy of the proposed method and can serve as the benchmarks. Our study provides a practical approach and can be extended to other scattering problems. This paper continues our previous study on the computation method for scattering poles of sound-soft obstacles.
{"title":"Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions","authors":"Xiaodong Liu , Jiguang Sun , Lei Zhang","doi":"10.1016/j.wavemoti.2024.103425","DOIUrl":"10.1016/j.wavemoti.2024.103425","url":null,"abstract":"<div><div>We propose a computation method for scattering poles of impedance obstacles. Boundary integral equations are used to formulate the problem. It is shown that the scattering poles are the eigenvalues of some integral operator. Then we employ the Nyström method to discretize the integral operator and obtain a nonlinear matrix eigenvalue problem. The eigenvalues are computed using a multistep parallel spectral indicator method. Numerical examples demonstrate the high accuracy of the proposed method and can serve as the benchmarks. Our study provides a practical approach and can be extended to other scattering problems. This paper continues our previous study on the computation method for scattering poles of sound-soft obstacles.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103425"},"PeriodicalIF":2.1,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552651","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 : 2024-10-22DOI: 10.1016/j.wavemoti.2024.103423
Xinru Guo, Wentao Li, Biao Li
This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of similarly-velocity lump chains approach infinity directly. The second pathway first transforms normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to , while between weakly interacting lump waves is proportional to . These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.
本文介绍了将Yu-Toda-Sasa-Fukuyama方程的正常相互作用块链退化为弱相互作用块波的两种不同途径，这将丰富块链与弱相互作用块波之间的相关性。第一种途径是让 M 个速度相似的块状链的周期直接接近无穷大。第二种途径首先将 M 个正常相互作用的块状链转化为具有相似动态行为的弱相互作用块状链。然后，通过让它们的周期接近无穷大，产生 MM+12 弱相互作用的块状波。在这个方程中，弱相互作用块链之间的距离与 ln|t| 成正比，而弱相互作用块波之间的距离与 |t|3 成正比。这些发现将为波浪理论、海洋科学及相关学科的研究提供宝贵的理论启示。
{"title":"Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains","authors":"Xinru Guo, Wentao Li, Biao Li","doi":"10.1016/j.wavemoti.2024.103423","DOIUrl":"10.1016/j.wavemoti.2024.103423","url":null,"abstract":"<div><div>This paper introduces two distinct pathways for degenerating normally interacting lump chains into weakly interacting lump waves for Yu–Toda–Sasa–Fukuyama equation, which will enrich the correlation between lump chains and weakly interacting lump waves. The first pathway involves letting the periods of <span><math><mi>M</mi></math></span> similarly-velocity lump chains approach infinity directly. The second pathway first transforms <span><math><mi>M</mi></math></span> normally interacting lump chains into weakly interacting lump chains with similar dynamic behaviors. Then, by allowing their periods to approach infinity, <span><math><mfrac><mrow><mi>M</mi><mfenced><mrow><mi>M</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> weakly interacting lump waves are produced. Distance between weakly interacting lump chains in this equation is proportional to <span><math><mrow><mo>ln</mo><mo>|</mo><mi>t</mi><mo>|</mo></mrow></math></span>, while between weakly interacting lump waves is proportional to <span><math><mroot><mrow><mo>|</mo><mi>t</mi><mo>|</mo></mrow><mrow><mn>3</mn></mrow></mroot></math></span>. These findings will contribute valuable theoretical insights to the study of wave theory, ocean science and related disciplines.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103423"},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552650","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 : 2024-10-22DOI: 10.1016/j.wavemoti.2024.103427
Philip Rosenau , Alexander Oron
We introduce and study a class of doubly sublinear Gardner equations where , which for induce solitons and in the doubly sublinear cases wherein , bi-directional compactons propagating in either direction. Their emergence, evolution, chase and head-on interactions are studied.
{"title":"Compactons in a class of doubly sublinear Gardner equations","authors":"Philip Rosenau , Alexander Oron","doi":"10.1016/j.wavemoti.2024.103427","DOIUrl":"10.1016/j.wavemoti.2024.103427","url":null,"abstract":"<div><div>We introduce and study a class of doubly sublinear Gardner equations <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>F</mi><msub><mrow><mrow><mo>(</mo><mi>u</mi><mo>;</mo><mi>n</mi><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mo>+</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>3</mn><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span> where <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>;</mo><mi>n</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>n</mi></mrow></msup><mo>−</mo><msub><mrow><mi>κ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>2</mn><mi>n</mi></mrow></msup></mrow></math></span>, which for <span><math><mrow><mn>0</mn><mo><</mo><mi>n</mi></mrow></math></span> induce solitons and in the doubly sublinear cases wherein <span><math><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo><</mo><mi>n</mi><mo><</mo><mn>0</mn></mrow></math></span>, <em>bi-directional</em> compactons propagating in either direction. Their emergence, evolution, chase and head-on interactions are studied.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103427"},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531508","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 : 2024-10-22DOI: 10.1016/j.wavemoti.2024.103424
José M. Carcione , Jing Ba
The quality factor is a dimensionless measure of the energy loss per cycle of wave modes in an attenuation medium. Accurate measurement is important in various fields, from seismological studies to detect zones of partial melting to the geophysics of reservoirs to study rock properties such as porosity, fluid properties and saturation and permeability. In seismology, the quality factors measured for normal (standing) modes and propagating waves differ, as well those of equivalent experiments based on resonant rods and ultrasonic pulses performed in the laboratory. These measurements result in temporal and spatial quality factors respectively. A relationship between these two different quality factors and between the corresponding attenuation factors was proposed by Knopoff et al. sixty years ago. The conversion factor is basically the ratio between the phase velocity and the group velocity, while for the attenuation factor is the group velocity. We test these relations, which hold for low-loss solids, for body waves, using a Kelvin–Voigt rheology and a constant model, which provide explicit expressions of the temporal and spatial quality factors and velocities involved in these relations. The proposed theory provides the basis for a complete characterization of temporal and spatial quality factors and velocity dispersion based on arbitrary stress–strain relationships.
{"title":"Test of the relation between temporal and spatial Q by Knopoff et al.","authors":"José M. Carcione , Jing Ba","doi":"10.1016/j.wavemoti.2024.103424","DOIUrl":"10.1016/j.wavemoti.2024.103424","url":null,"abstract":"<div><div>The quality factor is a dimensionless measure of the energy loss per cycle of wave modes in an attenuation medium. Accurate measurement is important in various fields, from seismological studies to detect zones of partial melting to the geophysics of reservoirs to study rock properties such as porosity, fluid properties and saturation and permeability. In seismology, the quality factors measured for normal (standing) modes and propagating waves differ, as well those of equivalent experiments based on resonant rods and ultrasonic pulses performed in the laboratory. These measurements result in temporal and spatial quality factors respectively. A relationship between these two different quality factors and between the corresponding attenuation factors was proposed by Knopoff et al. sixty years ago. The conversion factor is basically the ratio between the phase velocity and the group velocity, while for the attenuation factor is the group velocity. We test these relations, which hold for low-loss solids, for body waves, using a Kelvin–Voigt rheology and a constant <span><math><mi>Q</mi></math></span> model, which provide explicit expressions of the temporal and spatial quality factors and velocities involved in these relations. The proposed theory provides the basis for a complete characterization of temporal and spatial quality factors and velocity dispersion based on arbitrary stress–strain relationships.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103424"},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552652","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 : 2024-10-22DOI: 10.1016/j.wavemoti.2024.103426
Liu Yang, Ben Gao
In this paper, we research the fractional coupled Hirota equations with variable coefficients describing the collisions of two waves in deep oceans and the propagation of ultrashort light pulses in birefringent fibers and successfully acquire the double-hump one-soliton, two-solitons and N-solitons solutions via the Hirota bilinear method. At the same time, the Bäcklund transformation and the corresponding soliton solutions are also obtained. Based on the precise forms of the solitons solutions, we gain double-hump solitons images with different shapes including U-shape, V-shape and wave-type by assigning proper functions to the group velocity dispersion and the third-order dispersion and analyze the interaction dynamics of double-hump solitons. It is worth noting that the Hirota bilinear operators involved here are fractional rather than integer, which has never appeared in previous literatures.
本文研究了描述深海中两波碰撞和超短光脉冲在双折射光纤中传播的分数耦合可变系数 Hirota 方程，并通过 Hirota 双线性方法成功获得了双驼峰单孤子、双孤子和 N 孤子解。同时，还获得了贝克隆变换和相应的孤子解。在孤子解的精确形式基础上，通过给群速度色散和三阶色散赋予适当的函数，我们得到了不同形状的双驼峰孤子图像，包括 U 型、V 型和波型，并分析了双驼峰孤子的相互作用动力学。值得注意的是，这里涉及的 Hirota 双线性算子是分数算子而不是整数算子，这在以往的文献中从未出现过。
{"title":"The dynamic behaviors between double-hump solitons in birefringent fibers","authors":"Liu Yang, Ben Gao","doi":"10.1016/j.wavemoti.2024.103426","DOIUrl":"10.1016/j.wavemoti.2024.103426","url":null,"abstract":"<div><div>In this paper, we research the fractional coupled Hirota equations with variable coefficients describing the collisions of two waves in deep oceans and the propagation of ultrashort light pulses in birefringent fibers and successfully acquire the double-hump one-soliton, two-solitons and <em>N</em>-solitons solutions via the Hirota bilinear method. At the same time, the Bäcklund transformation and the corresponding soliton solutions are also obtained. Based on the precise forms of the solitons solutions, we gain double-hump solitons images with different shapes including U-shape, V-shape and wave-type by assigning proper functions to the group velocity dispersion and the third-order dispersion and analyze the interaction dynamics of double-hump solitons. It is worth noting that the Hirota bilinear operators involved here are fractional rather than integer, which has never appeared in previous literatures.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103426"},"PeriodicalIF":2.1,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531507","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 : 2024-10-19DOI: 10.1016/j.wavemoti.2024.103418
John Lekner
A family of solutions of the wave equation is presented. The simplest waveforms represent sub-cycle pulses; oscillatory pulses with a dominant wavenumber are also discussed. These solutions are sufficiently localized to have finite energy, momentum, and angular momentum when applied to acoustic and electromagnetic pulses. The energy, momentum, and angular momentum of the pulses are simply expressed in terms of the wavenumber weight function.
{"title":"Localized solutions of the wave equation","authors":"John Lekner","doi":"10.1016/j.wavemoti.2024.103418","DOIUrl":"10.1016/j.wavemoti.2024.103418","url":null,"abstract":"<div><div>A family of solutions of the wave equation is presented. The simplest waveforms represent sub-cycle pulses; oscillatory pulses with a dominant wavenumber are also discussed. These solutions are sufficiently localized to have finite energy, momentum, and angular momentum when applied to acoustic and electromagnetic pulses. The energy, momentum, and angular momentum of the pulses are simply expressed in terms of the wavenumber weight function.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103418"},"PeriodicalIF":2.1,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-19DOI: 10.1016/j.wavemoti.2024.103431
Ting Wang , Huachang Cui , Jingyu Zhang , Hanbei Guo , Meixia Chen
A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.
{"title":"Longitudinal wave propagation in a practical metamaterial lattice","authors":"Ting Wang , Huachang Cui , Jingyu Zhang , Hanbei Guo , Meixia Chen","doi":"10.1016/j.wavemoti.2024.103431","DOIUrl":"10.1016/j.wavemoti.2024.103431","url":null,"abstract":"<div><div>A practical metamaterial lattice is constructed by integrating curved beams, four-link mechanisms, and cantilever beams with lumped masses. It can generate two complete low-frequency bandgaps due to the lateral local resonance, inertia mass, and the main chain. The effective mass density and stiffness are obtained using different effective models, which show negative within the bandgaps. The analysis of the energy distribution and the space wave attenuation reveals that the metamaterial can attenuate the elastic waves in an exponential form within the bandgaps along the lattice. The finite element model is established to show the dynamic behaviour of the elastic wave propagation in the frequency domain and transient domain. Both results show that waves can be efficiently blocked within the bandgaps, while outside the bandgaps, waves can propagate without any attenuation. Finally, the experimental model of practical metamaterial is constructed, and the test piece is excited by a force hammer. Experimental results verify that the practical metamaterial can efficiently suppress the vibration within the bandgap frequency and validate the accuracy of the theoretical prediction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103431"},"PeriodicalIF":2.1,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593082","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 : 2024-10-16DOI: 10.1016/j.wavemoti.2024.103422
Didier Felbacq, Anthony Gourdin, Emmanuel Rousseau
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.
{"title":"A single layer representation of the scattered field for multiple scattering problems","authors":"Didier Felbacq, Anthony Gourdin, Emmanuel Rousseau","doi":"10.1016/j.wavemoti.2024.103422","DOIUrl":"10.1016/j.wavemoti.2024.103422","url":null,"abstract":"<div><div>The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103422"},"PeriodicalIF":2.1,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The global solvability in time and the potential for blow-up of solutions to non-integrable focusing nonlinear Schrödinger equations with nonzero boundary conditions at infinity present challenges that are less explored and understood compared to the case of zero boundary conditions. In this work, we address these questions by establishing estimates on the lifespan of solutions to non-integrable equations involving a general class of nonlinearities. These estimates depend on the size of the initial data, the growth of the nonlinearity, and relevant quantities associated with the amplitude of the background. The estimates provide quantified upper bounds for the minimum guaranteed lifespan of solutions. Qualitatively, for small initial data and background, these upper bounds suggest long survival times consistent with global existence of solutions. On the other hand, for larger initial data and background, the estimates indicate the potential for the intriguing phenomenon of instantaneous collapse in finite time. These qualitative theoretical results are illustrated via numerical simulations. Furthermore, importantly, the numerical findings motivate the proof of improved theoretical upper bounds that provide excellent quantitative agreement with the order of the numerically identified lifespan of solutions.
{"title":"On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrödinger equations","authors":"Dirk Hennig , Nikos I. Karachalios , Dionyssios Mantzavinos , Dimitrios Mitsotakis","doi":"10.1016/j.wavemoti.2024.103419","DOIUrl":"10.1016/j.wavemoti.2024.103419","url":null,"abstract":"<div><div>The global solvability in time and the potential for blow-up of solutions to non-integrable focusing nonlinear Schrödinger equations with nonzero boundary conditions at infinity present challenges that are less explored and understood compared to the case of zero boundary conditions. In this work, we address these questions by establishing estimates on the lifespan of solutions to non-integrable equations involving a general class of nonlinearities. These estimates depend on the size of the initial data, the growth of the nonlinearity, and relevant quantities associated with the amplitude of the background. The estimates provide quantified upper bounds for the minimum guaranteed lifespan of solutions. Qualitatively, for small initial data and background, these upper bounds suggest long survival times consistent with global existence of solutions. On the other hand, for larger initial data and background, the estimates indicate the potential for the intriguing phenomenon of instantaneous collapse in finite time. These qualitative theoretical results are illustrated via numerical simulations. Furthermore, importantly, the numerical findings motivate the proof of improved theoretical upper bounds that provide excellent quantitative agreement with the order of the numerically identified lifespan of solutions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103419"},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.wavemoti.2024.103421
Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes
The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.
应用广义特征函数展开法（GEM）和奇异性展开法（SEM）求解了时域中无限拉伸弦上波散射的典型问题。在没有散射体存在的情况下，GEM 与达朗贝尔公式等价；在点质量散射体与弹簧耦合的情况下，也推导出了 GEM。离散 GEM 是对离散傅立叶变换的概括，证明它可以简化为矩阵乘法。由傅立叶变换和残差定理推导出的 SEM 也被用于解决质量-弹簧系统的散射问题。此外，GEM 和 SEM 还被用于解决与锚点保持固定距离的质量的波散射问题，它支持更复杂的共振行为。
{"title":"Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems","authors":"Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes","doi":"10.1016/j.wavemoti.2024.103421","DOIUrl":"10.1016/j.wavemoti.2024.103421","url":null,"abstract":"<div><div>The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103421"},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号