Wave Motion最新文献

{"title":"Generalized analytical solutions of a Korteweg–de Vries (KdV) equation with arbitrary real coefficients: Association with the plasma-fluid framework and physical interpretation","authors":"Kuldeep Singh ,&nbsp;Ioannis Kourakis","doi":"10.1016/j.wavemoti.2024.103443","DOIUrl":"10.1016/j.wavemoti.2024.103443","url":null,"abstract":"<div><div>The Korteweg–de Vries (KdV) equation can be derived from a plasma-fluid model via a reductive perturbation technique. The associated methodology is summarized, from first principles, focusing on the underlying physical assumptions involved in the plasma-theoretical framework. A beam permeated electron-ion plasma is assumed, although the main findings of this study may be extended to more complicated plasma configurations. Rather counter-intuitively, it is shown that either of the (two) real coefficients appearing in the KdV equation (actually, both depending parametrically on the plasma configuration and on the beam characteristics) may take either positive or negative values, a possibility overlooked in the past. Different possibilities are investigated, from first principles, regarding the sign of the nonlinearity coefficient <span><math><mi>A</mi></math></span> (that is determined by the electron background statistics, in combination with the beam velocity) and the sign of the dispersion coefficient <span><math><mi>B</mi></math></span> (that is solely determined by the beam velocity and is always positive in its absence). The possibility of polarity reversal is investigated from first principles, in relation with both the electrostatic potential (pulse) profile and its associated electric field (bipolar pulse) <span><math><mrow><mi>E</mi><mo>=</mo><mo>−</mo><mo>∇</mo><mi>ϕ</mi></mrow></math></span> in the electrostatic approximation. Different types of excitations are shown to exist and the role of the (sign of the) various coefficients in the pulse-shaped solution’s propagation characteristics is discussed.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103443"},"PeriodicalIF":2.1,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650918","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}

{"title":"Oblique wave propagation over uneven flexible base in a fluid having free-surface tension","authors":"Balaram Sahu ,&nbsp;Smrutiranjan Mohapatra ,&nbsp;Manas Ranjan Sarangi","doi":"10.1016/j.wavemoti.2024.103433","DOIUrl":"10.1016/j.wavemoti.2024.103433","url":null,"abstract":"<div><div>A hydroelastic model has been introduced to study the impact of free surface tension on the propagation of oblique incident waves over small distortions on a thin, flexible floor of a fluid region. There are two varieties of time-harmonic propagating waves (free-surface and flexural modes) that exist in the region in the case of any specific frequency. One variety of proliferating waves having smaller wavenumber spreads on the top surface, while another spreads along the thin, flexible base. Using perturbation expansion involving a small parameter <span><math><mi>ϵ</mi></math></span>, the primary boundary value problem (<span>bvp</span>) is converted to a new <span>bvp</span> for the first-order approximation of the potential function. Subsequently, employing the Fourier transform approach, the first-order approximation of reflected and transmitted energy are acquired in the case of both modes of waves. Two specific examples of irregular floor are taken up to validate the theoretical outcomes flourished in this study. The influence of free-surface tension and flexible floor on the oblique wave propagation over uneven floor are analyzed and depicted graphically for certain sets of parametric values involved in the problem. The presence of free-surface tension on the upper boundary of the fluid introduces a third-order linearized boundary condition into the formulation of the wave-structure interaction problem, unlike the usual homogeneous first-order condition applicable for a free-surface. When a series of obliquely incident waves corresponding to free-surface and flexural modes spread over an irregular flexible floor of the fluid, the free-surface tension acts as a resistive force to the surface gravity waves. It can be inferred from this that the influence of surface tension at the free-surface of the fluid should not always be overlooked while dealing with the linear wave-structure interaction problem. Further, numerical estimation of reflected and transmitted energy for both varieties of time-harmonic waves are presented to confirm the analytical forms of energy relations almost accurately.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103433"},"PeriodicalIF":2.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650916","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":"Nonlinear incompressible shear wave models in hyperelasticity and viscoelasticity frameworks, with applications to Love waves","authors":"Shawn Samuel Carl McAdam,&nbsp;Samuel Opoku Agyemang,&nbsp;Alexei Cheviakov","doi":"10.1016/j.wavemoti.2024.103434","DOIUrl":"10.1016/j.wavemoti.2024.103434","url":null,"abstract":"<div><div>General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For the Murnaghan constitutive model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives <span><math><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi><mi>t</mi></mrow></msub></math></span> of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analysed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition <span><math><mrow><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><mfenced><mrow><mi>v</mi></mrow></mfenced><mo>&lt;</mo><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, while tending to the larger material wave speed <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> or <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> for large times.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103434"},"PeriodicalIF":2.1,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650910","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}

{"title":"Scorer beams in highly nonlocal media with a nonlinearity coefficient and an external potential","authors":"Wei-Ping Zhong ,&nbsp;Milivoj Belić ,&nbsp;Zhengping Yang","doi":"10.1016/j.wavemoti.2024.103442","DOIUrl":"10.1016/j.wavemoti.2024.103442","url":null,"abstract":"<div><div>The Snyder-Mitchell model of accessible solitons is a simple model that reduces the dynamics of solitons in highly nonlocal nonlinear media to a linear dynamical system with harmonic potential. Utilizing this model in a system with a nonlinearity coefficient and an external potential generated in highly nonlocal media, we explore its solution by the methods of variable separation and self-similar transformation. We discover a special solution of the model that includes Scorer functions, for which reason we call it the Scorer beam. The transmission dynamics of the Scorer beam in strongly nonlocal nonlinear media is analytically and numerically investigated. Under the specific condition of applying an exponential truncation factor, the evolution of the Scorer beam is more stable and converges faster. We also find that the Scorer beam exhibits self-bending and self-healing characteristics. Our results provide theoretical and numerical guidance for generating Scorer beams that might prove useful for future experimental exploration.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103442"},"PeriodicalIF":2.1,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142650917","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":"Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation","authors":"Antonio Schiavone ,&nbsp;Xiaodong Wang","doi":"10.1016/j.wavemoti.2024.103432","DOIUrl":"10.1016/j.wavemoti.2024.103432","url":null,"abstract":"<div><div>Elastic metamaterials are typically periodic materials possessing unit cells endowed with engineered architecture much smaller than the typical phenomenological length scale. The development of continuum models capable of accurately representing the effects of this aforementioned architecture is extremely challenging, and hence a sparsely developed area. This paper develops a novel 2-D continuum model capable of capturing the dynamic behaviour of a class of anisotropic elastic metamaterials with local rotational elements in the long wavelength limit. A constitutive relation incorporating these local rotational effects is proposed, and ratified using a representative discrete model using linear Hookean springs and identical rigid disks. The new continuum model is used to generate a dispersion relation for harmonic plane waves propagating in an arbitrary direction, which is subsequently compared to the dispersion behaviour of the original discrete model. The general behaviour of this continuum when subjected to 2-D planar harmonic wave propagation in the anisotropic medium is then analysed, with specific attention given to the effect of material anisotropy and wave propagation direction. This work is the first of its kind to create a new continuum model of a class of anisotropic elastic metamaterials with local rotational effects.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103432"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572515","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}

{"title":"On peridynamic acoustics","authors":"P.A. Martin","doi":"10.1016/j.wavemoti.2024.103429","DOIUrl":"10.1016/j.wavemoti.2024.103429","url":null,"abstract":"<div><div>We consider a nonlocal (peridynamic) version of the classical forced wave equation. This scalar three-dimensional equation contains a weight function (the “micromodulus”) and a length parameter (the “horizon”) that have to be selected. We investigate various properties (the locality limit as the horizon shrinks, plane waves and group velocity), paying attention to how these properties depend on the choice of the micromodulus. We solve the forced peridynamic equation in the static case (avoiding divergent integrals) and in the time-harmonic case (with a radiation condition, when needed).</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103429"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572507","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}

{"title":"Elastic coupled phase theory based on the Cosserat equations: Propagation of coherent waves","authors":"Alverède Simon,&nbsp;Tony Valier-Brasier,&nbsp;Jean-Marc Conoir","doi":"10.1016/j.wavemoti.2024.103430","DOIUrl":"10.1016/j.wavemoti.2024.103430","url":null,"abstract":"<div><div>We develop a new coupled phase theory (CPT) in order to model the propagation of elastic coherent waves in homogeneous solid media containing randomly distributed spherical elastic inclusions. To this end, the Buyevich’s theory previously developed for fluid media (Buyevich and Shchelchkova, 1978) has been adapted and applied to the Cosserat equations. A key point is to introduce the Independent Scattering Approximation (ISA). We show that the coherent wavenumbers depend explicitly on the external force applied to spheres, the torque characterizing their rotation and the stresslet which is the result of the resistance of the particles to the straining motion. Numerical results are in good agreement with experimental data.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103430"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578004","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":"Accurate computation of scattering poles of acoustic obstacles with impedance boundary conditions","authors":"Xiaodong Liu ,&nbsp;Jiguang Sun ,&nbsp;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}

{"title":"Derivation of weakly interacting lumps for the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation via degeneracy of lump chains","authors":"Xinru Guo,&nbsp;Wentao Li,&nbsp;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}

{"title":"Compactons in a class of doubly sublinear Gardner equations","authors":"Philip Rosenau ,&nbsp;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>&lt;</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>&lt;</mo><mi>n</mi><mo>&lt;</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}