Studies in Applied Mathematics最新文献_第9页

Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method 用一种新的 ODE 简化方法求解 gKdV-Schrödinger 耦合系统的精确孤波

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-11-04 DOI: 10.1111/sapm.12768

Stephen C. Anco, James Hornick, Sicheng Zhao, Thomas Wolf

{"title":"Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method","authors":"Stephen C. Anco, James Hornick, Sicheng Zhao, Thomas Wolf","doi":"10.1111/sapm.12768","DOIUrl":"https://doi.org/10.1111/sapm.12768","url":null,"abstract":"A new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 <mo>,</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$p=1,2,3,4$</annotation>\u0000 </semantics></math>. No solutions for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>></mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;1$</annotation>\u0000 </semantics></math> were known previously in the literature. For <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p=1$</annotation>\u0000 </semantics></math>, four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations as well as to nonlinear ODE systems of generalized Hénon–Heiles form.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12768","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rogue wave patterns associated with Adler–Moser polynomials featuring multiple roots in the nonlinear Schrödinger equation 非线性薛定谔方程中与具有多根特征的阿德勒-莫泽多项式相关的流波模式

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-28 DOI: 10.1111/sapm.12782

Huian Lin, Liming Ling

{"title":"Rogue wave patterns associated with Adler–Moser polynomials featuring multiple roots in the nonlinear Schrödinger equation","authors":"Huian Lin, Liming Ling","doi":"10.1111/sapm.12782","DOIUrl":"https://doi.org/10.1111/sapm.12782","url":null,"abstract":"In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including modified claw-like, one triple root (OTR)-type, modified OTR-type, two triple roots (TTR)-type, semimodified TTR-type, and modified TTR-type patterns. A correlation is established between these rogue wave patterns and the root structures of the Adler–Moser polynomials with multiple roots. At the positions in the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x,t)$</annotation>\u0000 </semantics></math>-plane corresponding to simple roots of the Adler–Moser polynomials, these high-order rogue wave patterns asymptotically approach first-order rogue waves. At the positions in the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(x,t)$</annotation>\u0000 </semantics></math>-plane corresponding to multiple roots of the Adler–Moser polynomials, these rogue wave patterns asymptotically tend toward lower-order fundamental rogue waves, dispersed first-order rogue waves, or mixed structures of these rogue waves. These structures are related to the root structures of special Adler–Moser polynomials with new free parameters, such as the Yablonskii–Vorob'ev polynomial hierarchy, among others. Notably, the positions of the fundamental lower-order rogue waves or mixed structures in these rogue wave patterns can be controlled freely under specific conditions.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Orthogonal Laurent Polynomials of Two Real Variables 两个实变量的正交劳伦多项式

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-26 DOI: 10.1111/sapm.12783

Ruymán Cruz-Barroso, Lidia Fernández

{"title":"Orthogonal Laurent Polynomials of Two Real Variables","authors":"Ruymán Cruz-Barroso, Lidia Fernández","doi":"10.1111/sapm.12783","DOIUrl":"https://doi.org/10.1111/sapm.12783","url":null,"abstract":"In this paper, we consider an appropriate ordering of the Laurent monomials <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>x</mi>\u0000 <mi>i</mi>\u0000 </msup>\u0000 <msup>\u0000 <mi>y</mi>\u0000 <mi>j</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$x^{i}y^{j}$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>i</mi>\u0000 <mo>,</mo>\u0000 <mi>j</mi>\u0000 <mo>∈</mo>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$i,j in mathbb {Z}$</annotation>\u0000 </semantics></math> that allows us to study sequences of orthogonal Laurent polynomials of the real variables <math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>y</mi>\u0000 <annotation>$y$</annotation>\u0000 </semantics></math> with respect to a positive Borel measure <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> defined on <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mo>{</mo>\u0000 <mi>x</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 <mo>∪</mo>\u0000 <mo>{</mo>\u0000 <mi>y</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 <mo>}</mo>\u0000 <mo>)</mo>\u0000 <mo>∩</mo>\u0000 <mi>supp</mi>\u0000 <mo>(</mo>\u0000 <mi>μ</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>∅</mi>\u0000 </mrow>\u0000 <annotation>$(lbrace x=0 rbrace cup lbrace y=0 rbrace) cap textrm {supp}(mu)= emptyset$</annotation>\u0000 </semantics></math>. This ordering is suitable for considering the multiplication plus inverse multiplication operator on each variable <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>+</mo>\u0000 <mfrac>\u0000 ","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12783","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rich dynamics of a hepatitis C virus infection model with logistic proliferation and time delays 具有逻辑增殖和时间延迟的丙型肝炎病毒感染模型的丰富动态变化

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-26 DOI: 10.1111/sapm.12781

Ke Guo, Wanbiao Ma

{"title":"Rich dynamics of a hepatitis C virus infection model with logistic proliferation and time delays","authors":"Ke Guo, Wanbiao Ma","doi":"10.1111/sapm.12781","DOIUrl":"https://doi.org/10.1111/sapm.12781","url":null,"abstract":"In this paper, we study a dynamic model of hepatitis C virus (HCV) infection with density-dependent proliferation of uninfected and infected hepatocytes and two time delays, which is derived from a three-dimensional model by the quasi-steady-state approximation. The model can exhibit forward bifurcation or backward bifurcation, and an explicit control threshold parameter <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>c</mi>\u0000 </msub>\u0000 <annotation>$R_c$</annotation>\u0000 </semantics></math> is obtained for the case of backward bifurcation. It is shown that if the proliferation rate of infected hepatocytes is greater than the proliferation rate of uninfected hepatocytes by a certain amount, it becomes more difficult for the virus to be removed. The model has rich dynamical properties: (i) In some parameter regions, bistability can occur; (ii) both time delays <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$tau _{1}$</annotation>\u0000 </semantics></math> (virus-to-cell delay) and <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$tau _{2}$</annotation>\u0000 </semantics></math> (cell-to-cell delay) can lead to Hopf bifurcations; (iii) same length of time delays <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$tau _{1}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>τ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$tau _{2}$</annotation>\u0000 </semantics></math> can lead to at most one stability switch, but different time delays can lead to multiple stability switches. Several sufficient conditions for the global stability of the disease-free equilibrium and the endemic equilibrium are obtained for both forward and backward bifurcation scenarios. In particular, several sharp results on global stability are obtained. Theoretical and numerical results portray the complexity of viral evolutionary dynamics in chronic HCV-infected patients.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Explicit exact solutions for plane shock waves in dilute polyatomic gases 稀释多原子气体中平面冲击波的显式精确解

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-25 DOI: 10.1111/sapm.12776

F. J. Uribe, R. M. Velasco, W. Marques Jr.

引用次数: 0

Efficient numerical approximations for a nonconservative nonlinear Schrödinger equation appearing in wind-forced ocean waves 风力海浪中出现的非保守非线性薛定谔方程的高效数值近似值

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-25 DOI: 10.1111/sapm.12774

Agissilaos Athanassoulis, Theodoros Katsaounis, Irene Kyza

引用次数: 0

Rigid lid limit in shallow water over a flat bottom 刚性盖子在平底浅水中的限制

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-25 DOI: 10.1111/sapm.12773

Benjamin Melinand

{"title":"Rigid lid limit in shallow water over a flat bottom","authors":"Benjamin Melinand","doi":"10.1111/sapm.12773","DOIUrl":"https://doi.org/10.1111/sapm.12773","url":null,"abstract":"We perform the so-called rigid lid limit on different shallow water models such as the abcd Bousssinesq systems or the Green–Naghdi equations. To do so, we consider an appropriate nondimensionalization of these models where two small parameters are involved: the shallowness parameter <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math> and a parameter <math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$epsilon$</annotation>\u0000 </semantics></math> which can be interpreted as a Froude number. When the parameter <math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$epsilon$</annotation>\u0000 </semantics></math> tends to zero, the surface deformation formally goes to the rest state, hence the name rigid lid limit. We carefully study this limit for different topologies. We also provide rates of convergence with respect to <math>\u0000 <semantics>\u0000 <mi>ε</mi>\u0000 <annotation>$epsilon$</annotation>\u0000 </semantics></math> and careful attention is given to the dependence on the shallowness parameter <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12773","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher-order integrable models for oceanic internal wave–current interactions 海洋内波-海流相互作用的高阶可积分模型

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-23 DOI: 10.1111/sapm.12778

David Henry, Rossen I. Ivanov, Zisis N. Sakellaris

{"title":"Higher-order integrable models for oceanic internal wave–current interactions","authors":"David Henry, Rossen I. Ivanov, Zisis N. Sakellaris","doi":"10.1111/sapm.12778","DOIUrl":"https://doi.org/10.1111/sapm.12778","url":null,"abstract":"In this paper, we derive a higher-order Korteweg–de Vries (HKdV) equation as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents by permitting a sheared current in both fluid layers, and also accommodates the effect of the Earth's rotation by including Coriolis forces (restricted to the Equatorial region). The resulting governing equations describing the water wave problem in two fluid layers under a “flat-surface” assumption are expressed in a general form as a system of two coupled equations through Dirichlet–Neumann (DN) operators. The DN operators also facilitate a convenient Hamiltonian formulation of the problem. We then derive the HKdV equation from this Hamiltonian formulation, in the long-wave, and small-amplitude, asymptotic regimes. Finally, it is demonstrated that there is an explicit transformation connecting the HKdV we derive with the following integrable equations of a similar type: KdV5, Kaup–Kuperschmidt equation, Sawada–Kotera equation, and Camassa–Holm and Degasperis–Procesi equations.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12778","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation 惠瑟姆调制理论与福卡斯-勒内尔斯方程黎曼问题解的分类

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-23 DOI: 10.1111/sapm.12779

Zhi-Jia Wu, Shou-Fu Tian

引用次数: 0

Hydrodynamics of a discrete conservation law 离散守恒定律的流体力学

IF 2.6 2区数学

Studies in Applied Mathematics Pub Date : 2024-10-23 DOI: 10.1111/sapm.12767

Patrick Sprenger, Christopher Chong, Emmanuel Okyere, Michael Herrmann, P. G. Kevrekidis, Mark A. Hoefer

{"title":"Hydrodynamics of a discrete conservation law","authors":"Patrick Sprenger, Christopher Chong, Emmanuel Okyere, Michael Herrmann, P. G. Kevrekidis, Mark A. Hoefer","doi":"10.1111/sapm.12767","DOIUrl":"https://doi.org/10.1111/sapm.12767","url":null,"abstract":"The Riemann problem for the discrete conservation law <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <msub>\u0000 <mover>\u0000 <mi>u</mi>\u0000 <mo>̇</mo>\u0000 </mover>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msubsup>\u0000 <mi>u</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>−</mo>\u0000 <msubsup>\u0000 <mi>u</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msubsup>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$2 dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$</annotation>\u0000 </semantics></math> is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogs of well-known dispersive hydrodynamic solutions—rarefaction waves (RWs) and dispersive shock waves (DSWs)—additional unsteady solution families and finite-time blowup are observed. Two solution types exhibit no known conservative continuum correlates: (i) a counterpropagating DSW and RW solution separated by a symmetric, stationary shock and (ii) an unsteady shock emitting two counterpropagating periodic wavetrains with the same frequency connected to a partial DSW or an RW. Another class of solutions called traveling DSWs, (iii), consists of a partial DSW connected to a traveling wave comprised of a periodic wavetrain with a rapid transition to a constant. Portions of solutions (ii) and (iii) are interpreted as shock solutions of the Whitham modulation equations.","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142642049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0