Pub Date : 2023-09-27DOI: 10.1007/s00033-023-02104-8
Marzia Romano
Abstract The three wave resonant interaction model (3WRI) is a non-dispersive system with quadratic coupling between the components that finds application in many areas, including nonlinear optics, fluids and plasma physics. Using its integrability, and in particular its Lax Pair representation, we carry out the linear stability analysis of the plane wave solutions interacting under resonant conditions when they are perturbed via localised perturbations. A topological classification of the so-called stability spectra is provided with respect to the physical parameters appearing both in the system itself and in its plane wave solution. Alongside the stability spectra, we compute the corresponding gain function, from which we deduce that this system is linearly unstable for any generic choice of the physical parameters. In addition to stability spectra of the same kind observed in the system of two coupled nonlinear Schrödinger equations, whose non-vanishing gain functions detect the occurrence of the modulational instability, the stability spectra of the 3WRI system possess new topological components, whose associated gain functions are different from those characterising the modulational instability. By drawing on a recent link between modulational instability and the occurrence of rogue waves, we speculate that linear instability of baseband-type can be a necessary condition for the onset of rogue wave types in the 3WRI system, thus providing a tool to predict the subsequent nonlinear evolution of the perturbation.
{"title":"The 3-wave resonant interaction model: spectra and instabilities of plane waves","authors":"Marzia Romano","doi":"10.1007/s00033-023-02104-8","DOIUrl":"https://doi.org/10.1007/s00033-023-02104-8","url":null,"abstract":"Abstract The three wave resonant interaction model (3WRI) is a non-dispersive system with quadratic coupling between the components that finds application in many areas, including nonlinear optics, fluids and plasma physics. Using its integrability, and in particular its Lax Pair representation, we carry out the linear stability analysis of the plane wave solutions interacting under resonant conditions when they are perturbed via localised perturbations. A topological classification of the so-called stability spectra is provided with respect to the physical parameters appearing both in the system itself and in its plane wave solution. Alongside the stability spectra, we compute the corresponding gain function, from which we deduce that this system is linearly unstable for any generic choice of the physical parameters. In addition to stability spectra of the same kind observed in the system of two coupled nonlinear Schrödinger equations, whose non-vanishing gain functions detect the occurrence of the modulational instability, the stability spectra of the 3WRI system possess new topological components, whose associated gain functions are different from those characterising the modulational instability. By drawing on a recent link between modulational instability and the occurrence of rogue waves, we speculate that linear instability of baseband-type can be a necessary condition for the onset of rogue wave types in the 3WRI system, thus providing a tool to predict the subsequent nonlinear evolution of the perturbation.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1007/s00033-023-02100-y
Shanbing Li, Mingxin Wang
{"title":"Global bifurcation of coexistence states for a prey-taxis system with homogeneous Dirichlet boundary conditions","authors":"Shanbing Li, Mingxin Wang","doi":"10.1007/s00033-023-02100-y","DOIUrl":"https://doi.org/10.1007/s00033-023-02100-y","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"483 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 10.1007/s00033-023-02095-6
Bing-Er Jiang, Fei-Ying Yang, Wan-Yue Tang
{"title":"Wave propagation for a non-cooperative system with nonlocal dispersal and a cyclic structure","authors":"Bing-Er Jiang, Fei-Ying Yang, Wan-Yue Tang","doi":"10.1007/s00033-023-02095-6","DOIUrl":"https://doi.org/10.1007/s00033-023-02095-6","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134887096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 10.1007/s00033-023-02096-5
Yaru Dou, Gang Meng, Zhe Zhou
{"title":"Continuity of periodic solutions for Lotka–Volterra equations in coefficient functions","authors":"Yaru Dou, Gang Meng, Zhe Zhou","doi":"10.1007/s00033-023-02096-5","DOIUrl":"https://doi.org/10.1007/s00033-023-02096-5","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134887194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1007/s00033-023-02094-7
M. Amar, D. Andreucci, C. Timofte
Abstract The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required.
摘要本文所分析的模型来源于对复合材料的描述，这种复合材料是由一层由两种不同材料的子层组成的薄层包裹的含有周期性夹杂物阵列的承载介质制成的。这种两相涂层材料在正交方向上具有较低的扩散系数，而在切向上具有较高的扩散系数。在之前的一篇论文(Amar In IFB 21:41-59, 2019)中，通过浓缩程序，内层被不完美的界面取代。本文通过周期展开的方法，研究了外涂层的浓度和均匀化问题，得到了一个远非标准的模型。尽管极限问题看起来像椭圆方程的经典狄利克雷问题，但在构造均匀矩阵和源项时，需要进行非常精细的分析。
{"title":"Interface potential in composites with general imperfect transmission conditions","authors":"M. Amar, D. Andreucci, C. Timofte","doi":"10.1007/s00033-023-02094-7","DOIUrl":"https://doi.org/10.1007/s00033-023-02094-7","url":null,"abstract":"Abstract The model analyzed in this paper has its origins in the description of composites made by a hosting medium containing a periodic array of inclusions coated by a thin layer consisting of sublayers of two different materials. This two-phase coating material is such that the external part has a low diffusivity in the orthogonal direction, while the internal one has high diffusivity along the tangential direction. In a previous paper (Amar in IFB 21:41–59, 2019), by means of a concentration procedure, the internal layer was replaced by an imperfect interface. The present paper is concerned with the concentration of the external coating layer and the homogenization, via the periodic unfolding method, of the resulting model, which is far from being a standard one. Despite the fact that the limit problem looks like a classical Dirichlet problem for an elliptic equation, in the construction of the homogenized matrix and of the source term, a very delicate analysis is required.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136310088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1007/s00033-023-02092-9
Hongliang Li, Yang Wang, Rong Yuan, Zhaohai Ma
{"title":"Traveling waves of predator–prey system with a sedentary predator","authors":"Hongliang Li, Yang Wang, Rong Yuan, Zhaohai Ma","doi":"10.1007/s00033-023-02092-9","DOIUrl":"https://doi.org/10.1007/s00033-023-02092-9","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136310081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1007/s00033-023-02091-w
Luca D’Errico
{"title":"A numerical study of the de Broglie gravitational wave of the electron","authors":"Luca D’Errico","doi":"10.1007/s00033-023-02091-w","DOIUrl":"https://doi.org/10.1007/s00033-023-02091-w","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136310093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-15DOI: 10.1007/s00033-023-02089-4
Robert Wegner
Abstract We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in $$(1 + H^s) times H^{s-1}$$ (1+Hs)×Hs-1 with $$s ge 1$$ s≥1 . We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross–Pitaevskii equation in Koch and Liao (Adv Math 377, 2021; Adv Math 420, 2023). Our core result is a local bilipschitz equivalence of the relevant function spaces, which enables the transfer of results between the two equations.
摘要建立了无真空条件下$$(1 + H^s) times H^{s-1}$$ (1 + H s) × H s - 1 ($$s ge 1$$ s≥1)下一维水动力Gross-Pitaevskii方程的全局时适性。我们通过Madelung变换将之前的Gross-Pitaevskii方程的全局时间适定性结果简化到Koch和Liao (Adv Math 377, 2021;Adv数学420,2023)。我们的核心结果是相关函数空间的局部bilipschitz等价，它使结果在两个方程之间传递。
{"title":"Global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations without vacuum","authors":"Robert Wegner","doi":"10.1007/s00033-023-02089-4","DOIUrl":"https://doi.org/10.1007/s00033-023-02089-4","url":null,"abstract":"Abstract We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in $$(1 + H^s) times H^{s-1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>H</mml:mi> <mml:mi>s</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> with $$s ge 1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross–Pitaevskii equation in Koch and Liao (Adv Math 377, 2021; Adv Math 420, 2023). Our core result is a local bilipschitz equivalence of the relevant function spaces, which enables the transfer of results between the two equations.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135435619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-15DOI: 10.1007/s00033-023-02085-8
Gelson C. G. dos Santos, Natan de Assis Lima, Romildo N. de Lima
{"title":"Existence of solution for a class of integro-differential sublinear problems with strong singularity","authors":"Gelson C. G. dos Santos, Natan de Assis Lima, Romildo N. de Lima","doi":"10.1007/s00033-023-02085-8","DOIUrl":"https://doi.org/10.1007/s00033-023-02085-8","url":null,"abstract":"","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135397102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-15DOI: 10.1007/s00033-023-02080-z
Noelia Bazarra, José R. Fernández, Ramón Quintanilla
Abstract In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter.
{"title":"A MGT thermoelastic problem with two relaxation parameters","authors":"Noelia Bazarra, José R. Fernández, Ramón Quintanilla","doi":"10.1007/s00033-023-02080-z","DOIUrl":"https://doi.org/10.1007/s00033-023-02080-z","url":null,"abstract":"Abstract In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135395731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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