In this paper, the Riemann–Hilbert (RH) method is developed to solve the Hirota–Satsuma coupled KdV (HScKdV) system associated with matrix spectral problem. Because the spectral matrix is asymmetric and high order, it brings great difficulties to analysis and solution. First, a direct scattering problem is carried out, from which the initial data are mapped to the scattering data. On the basis of introducing the generalized cross product of vectors, the basic meromorphic matrix eigenfunctions of corresponding Lax pairs are expressed by the Jost solutions and adjoint Jost solutions. Then, the inverse scattering problem is characterized as the matrix RH problem, which gives the formula for constructing solutions of the HScKdV system. As an example, the RH problem corresponding to the reflectionless case is solved and the soliton solution of the HScKdV system is obtained.
{"title":"Riemann–Hilbert Approach for the Hirota–Satsuma Coupled KdV System","authors":"Haibing Zhang, Xianguo Geng, Huan Liu","doi":"10.1111/sapm.70113","DOIUrl":"https://doi.org/10.1111/sapm.70113","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the Riemann–Hilbert (RH) method is developed to solve the Hirota–Satsuma coupled KdV (HScKdV) system associated with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>×</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$4times 4$</annotation>\u0000 </semantics></math> matrix spectral problem. Because the spectral matrix is asymmetric and high order, it brings great difficulties to analysis and solution. First, a direct scattering problem is carried out, from which the initial data are mapped to the scattering data. On the basis of introducing the generalized cross product of vectors, the basic meromorphic matrix eigenfunctions of corresponding Lax pairs are expressed by the Jost solutions and adjoint Jost solutions. Then, the inverse scattering problem is characterized as the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mo>×</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$4times 4$</annotation>\u0000 </semantics></math> matrix RH problem, which gives the formula for constructing solutions of the HScKdV system. As an example, the RH problem corresponding to the reflectionless case is solved and the soliton solution of the HScKdV system is obtained.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022156","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}
Beardsley, T., Behringer, M., & Komarova, N. L. (2025). Detecting (the Absence of) Species Interactions in Microbial Ecological Systems. Studies in Applied Mathematics, 154(2), e70009.
The funding statement for this article was missing. The below funding statement has been added to the article:
Support of NSF grants DMS 2435484 and MCB 2141651 is gratefully acknowledged.
We apologize for this error.
Beardsley， T., Behringer， M., & Komarova, n.l.（2025）。微生物生态系统中物种相互作用的检测（缺失）。应用数学研究，14 (2),e70009。这篇文章的资助声明缺失了。文章中添加了以下资助声明：感谢NSF拨款DMS 2435484和MCB 2141651的支持。我们为这个错误道歉。
{"title":"Correction to “Detecting (the Absence of) Species Interactions in Microbial Ecological Systems”","authors":"","doi":"10.1111/sapm.70107","DOIUrl":"https://doi.org/10.1111/sapm.70107","url":null,"abstract":"<p>Beardsley, T., Behringer, M., & Komarova, N. L. (2025). Detecting (the Absence of) Species Interactions in Microbial Ecological Systems. <i>Studies in Applied Mathematics</i>, <i>154</i>(2), e70009.</p><p>The funding statement for this article was missing. The below funding statement has been added to the article:</p><p>Support of NSF grants DMS 2435484 and MCB 2141651 is gratefully acknowledged.</p><p>We apologize for this error.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70107","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022158","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}
For the one-dimensional nonlinear Schrödinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of nonexistence and curves of stability change on the parameter planes.
{"title":"On Standing Waves of 1D Nonlinear Schrödinger Equation With Triple Power Nonlinearity","authors":"Theo Morrison, Tai-Peng Tsai","doi":"10.1111/sapm.70106","DOIUrl":"https://doi.org/10.1111/sapm.70106","url":null,"abstract":"<p>For the one-dimensional nonlinear Schrödinger equation with triple power nonlinearity and general exponents, we study analytically and numerically the existence and stability of standing waves. Special attention is paid to the curves of nonexistence and curves of stability change on the parameter planes.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70106","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022162","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}
We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005): 1627–1637]. The stochastic variational principle implies the existence of stochastic 1-form and 2-form conservation laws, as well as conservation laws arising from continuous variational symmetries via a stochastic Noether's theorem. These results are the stochastic analogs of those found in deterministic variational principles. Furthermore, we develop stochastic structure-preserving collocation methods for this class of stochastic multisymplectic systems. These integrators possess a discrete analog of the stochastic 2-form conservation law and, in the case of linear systems, also guarantee discrete momentum conservation. The effectiveness of the proposed methods is demonstrated through their application to stochastic nonlinear Schrödinger equations featuring either stochastic transport or stochastic dispersion.
{"title":"Stochastic Multisymplectic PDEs and Their Structure-Preserving Numerical Methods","authors":"Ruiao Hu, Linyu Peng","doi":"10.1111/sapm.70112","DOIUrl":"https://doi.org/10.1111/sapm.70112","url":null,"abstract":"<p>We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in Hydon [<i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, 461 (2005): 1627–1637]. The stochastic variational principle implies the existence of stochastic 1-form and 2-form conservation laws, as well as conservation laws arising from continuous variational symmetries via a stochastic Noether's theorem. These results are the stochastic analogs of those found in deterministic variational principles. Furthermore, we develop stochastic structure-preserving collocation methods for this class of stochastic multisymplectic systems. These integrators possess a discrete analog of the stochastic 2-form conservation law and, in the case of linear systems, also guarantee discrete momentum conservation. The effectiveness of the proposed methods is demonstrated through their application to stochastic nonlinear Schrödinger equations featuring either stochastic transport or stochastic dispersion.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70112","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022161","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}
In this paper, the classical and nonlocal semi-discrete nonlinear Schrödinger (sdNLS) equations with nonzero backgrounds are solved by means of the bilinearization-reduction approach. In the first step of this approach, the unreduced sdNLS system with a nonzero background is bilinearized and its solutions are presented in terms of quasi-double Casoratians. Then, reduction techniques are implemented to deal with complex and nonlocal reductions, which yields solutions for the four classical and nonlocal sdNLS equations with a plane wave background or a hyperbolic function background. These solutions are expressed with explicit formulae and allow classifications according to canonical forms of certain spectral matrix. In particular, we present explicit formulae for general rogue waves for the classical focusing sdNLS equation. Some obtained solutions are analyzed and illustrated.
{"title":"The Integrable Semi-Discrete Nonlinear Schrödinger Equations With Nonzero Backgrounds: Bilinearization-Reduction Approach","authors":"Xiao Deng, Kui Chen, Hongyang Chen, Da-jun Zhang","doi":"10.1111/sapm.70108","DOIUrl":"https://doi.org/10.1111/sapm.70108","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, the classical and nonlocal semi-discrete nonlinear Schrödinger (sdNLS) equations with nonzero backgrounds are solved by means of the bilinearization-reduction approach. In the first step of this approach, the unreduced sdNLS system with a nonzero background is bilinearized and its solutions are presented in terms of quasi-double Casoratians. Then, reduction techniques are implemented to deal with complex and nonlocal reductions, which yields solutions for the four classical and nonlocal sdNLS equations with a plane wave background or a hyperbolic function background. These solutions are expressed with explicit formulae and allow classifications according to canonical forms of certain spectral matrix. In particular, we present explicit formulae for general rogue waves for the classical focusing sdNLS equation. Some obtained solutions are analyzed and illustrated.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022159","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}
In this paper, we apply the viscosity–flux approximation method coupled with the maximum principle to obtain the a priori estimates for the viscosity approximation solutions of the unsteady isentropic gas flow in the de Laval nozzle. Then by applying the compensated compactness method, we obtain the global existence of entropy solutions. Finally, we study the large-time behavior of solutions and show the decay of the norm of density for any adiabatic exponent .
{"title":"Large-Time Existence and Decay of Entropy Solutions for Unsteady Isentropic Gas Flow in the Quasi-One-Dimensional Nozzle","authors":"Jianjun Chen, Qiquan Fang, Yun-guang Lu, Naoki Tsuge","doi":"10.1111/sapm.70104","DOIUrl":"https://doi.org/10.1111/sapm.70104","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we apply the viscosity–flux approximation method coupled with the maximum principle to obtain the a priori <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$L^{infty }$</annotation>\u0000 </semantics></math> estimates for the viscosity approximation solutions of the unsteady isentropic gas flow in the de Laval nozzle. Then by applying the compensated compactness method, we obtain the global existence of entropy solutions. Finally, we study the large-time behavior of solutions and show the decay of the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>γ</mi>\u0000 </msup>\u0000 <annotation>$L^{gamma }$</annotation>\u0000 </semantics></math> norm of density for any adiabatic exponent <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>></mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$gamma >1$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144998865","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}
Host mobility and environmental heterogeneity in vector populations are critical determinants of spatial patterns in mosquito-borne disease transmission. To investigate the impact of spatial heterogeneity and host dispersal on transmission dynamics, this manuscript proposes a partially degenerate nonlocal dispersal Ross–Macdonald model. The basic reproduction number is identified as a critical threshold that determines the global dynamics of the model. The analytical challenge of noncompact solution map of this partially degenerate nonlocal model is addressed using comparison arguments for the phase space of Lebesgue measurable and bounded functions. Furthermore, we characterize the asymptotic behavior of under small and large diffusion regimes, linking dispersal rates to transmission potential. Numerical simulations reveal how host mobility and spatially varying environment modulate disease persistence and transmission risks. Simulations also indicate that the model assuming local dispersal may underestimate transmission risks, and the epidemic size does not monotonically increase with .
{"title":"Global Dynamics of a Partially Degenerate Nonlocal Model for Mosquito-Borne Disease Transmission","authors":"Mengjie Han, Zhenguo Bai, Yijun Lou","doi":"10.1111/sapm.70101","DOIUrl":"https://doi.org/10.1111/sapm.70101","url":null,"abstract":"<div>\u0000 \u0000 <p>Host mobility and environmental heterogeneity in vector populations are critical determinants of spatial patterns in mosquito-borne disease transmission. To investigate the impact of spatial heterogeneity and host dispersal on transmission dynamics, this manuscript proposes a partially degenerate nonlocal dispersal Ross–Macdonald model. The basic reproduction number <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math> is identified as a critical threshold that determines the global dynamics of the model. The analytical challenge of noncompact solution map of this partially degenerate nonlocal model is addressed using comparison arguments for the phase space of Lebesgue measurable and bounded functions. Furthermore, we characterize the asymptotic behavior of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math> under small and large diffusion regimes, linking dispersal rates to transmission potential. Numerical simulations reveal how host mobility and spatially varying environment modulate disease persistence and transmission risks. Simulations also indicate that the model assuming local dispersal may underestimate transmission risks, and the epidemic size does not monotonically increase with <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathcal {R}_0$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891661","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}
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup–Boussinesq equations. We suggest a methodology for constructing a series of solutions for all systems in the family. The crux of the approach lies in reducing this system to a dispersionless integrable system which is a special case of linearly degenerate quasilinear systems actively explored since the 1990s and recently studied in the framework of Nijenhuis geometry. These infinite-dimensional integrable systems are closely connected to certain explicit finite-dimensional integrable systems. We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.
{"title":"Finite-Dimensional Reductions and Finite-Gap-Type Solutions of Multicomponent Integrable PDEs","authors":"Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev","doi":"10.1111/sapm.70100","DOIUrl":"https://doi.org/10.1111/sapm.70100","url":null,"abstract":"<p>The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg–de Vries, coupled KdV, Harry Dym, coupled Harry Dym, Camassa–Holm, multicomponent Camassa–Holm, Dullin–Gottwald–Holm, and Kaup–Boussinesq equations. We suggest a methodology for constructing a series of solutions for all systems in the family. The crux of the approach lies in reducing this system to a dispersionless integrable system which is a special case of linearly degenerate quasilinear systems actively explored since the 1990s and recently studied in the framework of Nijenhuis geometry. These infinite-dimensional integrable systems are closely connected to certain explicit finite-dimensional integrable systems. We provide a link between solutions of our multicomponent PDE systems and solutions of this finite-dimensional system, and use it to construct animations of multicomponent analogous of soliton and cnoidal solutions.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 2","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.70100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144881460","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}
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