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On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrödinger equations 论一类聚焦非线性薛定谔方程非零背景解的寿命
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-11 DOI: 10.1016/j.wavemoti.2024.103419
Dirk Hennig , Nikos I. Karachalios , Dionyssios Mantzavinos , Dimitrios Mitsotakis
{"title":"On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrödinger equations","authors":"Dirk Hennig ,&nbsp;Nikos I. Karachalios ,&nbsp;Dionyssios Mantzavinos ,&nbsp;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}
引用次数: 0
Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems 典型时域波散射问题的广义特征函数展开和奇异性展开方法
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-11 DOI: 10.1016/j.wavemoti.2024.103421
Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes
{"title":"Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems","authors":"Ben Wilks ,&nbsp;Michael H. Meylan ,&nbsp;Fabien Montiel ,&nbsp;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}
引用次数: 0
Natural frequencies of a Timoshenko beam with cracks 有裂缝的季莫申科梁的自然频率
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-10-06 DOI: 10.1016/j.wavemoti.2024.103420
E.I. Shifrin, I.M. Lebedev
{"title":"Natural frequencies of a Timoshenko beam with cracks","authors":"E.I. Shifrin,&nbsp;I.M. Lebedev","doi":"10.1016/j.wavemoti.2024.103420","DOIUrl":"10.1016/j.wavemoti.2024.103420","url":null,"abstract":"<div><div>A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103420"},"PeriodicalIF":2.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433958","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}
引用次数: 0
Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system 高阶非线性薛定谔-麦克斯韦-布洛赫系统的周期性背景上的游荡波
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-29 DOI: 10.1016/j.wavemoti.2024.103417
Jian Chang, Zhaqilao
{"title":"Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system","authors":"Jian Chang,&nbsp;Zhaqilao","doi":"10.1016/j.wavemoti.2024.103417","DOIUrl":"10.1016/j.wavemoti.2024.103417","url":null,"abstract":"<div><div>In this paper, we construct the rogue wave solutions on the background of the Jacobian elliptic functions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system. The Jacobian elliptic function traveling wave solutions as the seed solutions are considered. Through the approach of the nonlinearization of the Lax pair and Darboux transformation method, the rogue waves and the line rogue waves on the Jacobian elliptic functions dn and cn background are obtained, respectively.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103417"},"PeriodicalIF":2.1,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420738","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}
引用次数: 0
On the viscoelastic-electromagnetic-gravitational analogy 关于粘弹性-电磁-引力类比
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-19 DOI: 10.1016/j.wavemoti.2024.103411
José M. Carcione , Jing Ba
{"title":"On the viscoelastic-electromagnetic-gravitational analogy","authors":"José M. Carcione ,&nbsp;Jing Ba","doi":"10.1016/j.wavemoti.2024.103411","DOIUrl":"10.1016/j.wavemoti.2024.103411","url":null,"abstract":"<div><div>The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103411"},"PeriodicalIF":2.1,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441459","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}
引用次数: 0
The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory 弛豫对等温声学行波的影响：基于纳维-斯托克斯-麦克斯韦理论的新型可解模型
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103415
P.M. Jordan , A. Puri
{"title":"The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory","authors":"P.M. Jordan ,&nbsp;A. Puri","doi":"10.1016/j.wavemoti.2024.103415","DOIUrl":"10.1016/j.wavemoti.2024.103415","url":null,"abstract":"<div><div>An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103415"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315738","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}
引用次数: 0
Solitary wave solutions and their limits to the fractional Schrödinger system 分数薛定谔系统的孤波解及其极限
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103416
Guoyi Fu, Xiaoyan Chen, Shihui Zhu
{"title":"Solitary wave solutions and their limits to the fractional Schrödinger system","authors":"Guoyi Fu,&nbsp;Xiaoyan Chen,&nbsp;Shihui Zhu","doi":"10.1016/j.wavemoti.2024.103416","DOIUrl":"10.1016/j.wavemoti.2024.103416","url":null,"abstract":"<div><div>This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103416"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315737","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}
引用次数: 0
New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves 一些 (2+1) 维非线性演化方程和折叠波的新精确解
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-18 DOI: 10.1016/j.wavemoti.2024.103414
Kai Zhou , Sen-Yue Lou , Shou-Feng Shen
{"title":"New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves","authors":"Kai Zhou ,&nbsp;Sen-Yue Lou ,&nbsp;Shou-Feng Shen","doi":"10.1016/j.wavemoti.2024.103414","DOIUrl":"10.1016/j.wavemoti.2024.103414","url":null,"abstract":"<div><p>By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103414"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274165","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}
引用次数: 0
A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure 具有完整科里奥利力和漩涡结构的高维地球物理流体模型
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-14 DOI: 10.1016/j.wavemoti.2024.103410
Na Liu , Xiaojun Yin , Ruigang Zhang , Quansheng Liu
{"title":"A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure","authors":"Na Liu ,&nbsp;Xiaojun Yin ,&nbsp;Ruigang Zhang ,&nbsp;Quansheng Liu","doi":"10.1016/j.wavemoti.2024.103410","DOIUrl":"10.1016/j.wavemoti.2024.103410","url":null,"abstract":"<div><div>Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103410"},"PeriodicalIF":2.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319550","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}
引用次数: 0
Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields 强水平电场下具有恒定涡度的周期波下的流动结构
IF 2.1 3区 物理与天体物理
Wave Motion Pub Date : 2024-09-12 DOI: 10.1016/j.wavemoti.2024.103413
Marcelo V. Flamarion , Evgeny Kochurin , Roberto Ribeiro Jr , Nikolay Zubarev
{"title":"Flow structure beneath periodic waves with constant vorticity under strong horizontal electric fields","authors":"Marcelo V. Flamarion ,&nbsp;Evgeny Kochurin ,&nbsp;Roberto Ribeiro Jr ,&nbsp;Nikolay Zubarev","doi":"10.1016/j.wavemoti.2024.103413","DOIUrl":"10.1016/j.wavemoti.2024.103413","url":null,"abstract":"<div><p>While several articles have been written on Electrohydrodynamics (EHD) flows or flows with constant vorticity separately, little is known about the extent to which the combined effects of EHD and constant vorticity affect the flow. This study aims to shed light on this topic by investigating the combined influence of a horizontal electric field and constant vorticity on the free surface and the emergence of stagnation points. Using the Euler equations framework, we employ conformal mapping and pseudo-spectral numerical methods. Our findings reveal that increasing the electric field intensity eliminates stagnation points and smoothen the wave profile. This implies that a horizontal electric field acts as a mechanism for the elimination of stagnation points within the fluid body. Besides, we have identified regimes where three stagnation points appear on the free surface — something that cannot occur in purely gravity rotational waves.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103413"},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239396","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}
引用次数: 0
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