Studies in Applied Mathematics最新文献_第2页

Integrable Boundary Conditions for the Nonlinear Schrödinger Hierarchy Via the Fokas Method 基于Fokas方法的非线性Schrödinger层次的可积边界条件

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-16 DOI: 10.1111/sapm.70116

Baoqiang Xia

引用次数: 0

Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity 具有幂扩散系数的Kolmogorov倒向方程的惊人对称性和精确解

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1111/sapm.70105

Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych

{"title":"Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity","authors":"Serhii D. Koval, Elsa Dos Santos Cardoso-Bihlo, Roman O. Popovych","doi":"10.1111/sapm.70105","DOIUrl":"https://doi.org/10.1111/sapm.70105","url":null,"abstract":"<div>\u0000 \u0000 Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power diffusivity and solve the problems of their complete group classifications. The results on the equivalence groups are double-checked with the algebraic method. Within these classes, the remarkable Fokker–Planck and the fine Kolmogorov backward equations are distinguished by their exceptional symmetry properties. We extend the known results on these two equations to their counterparts with respect to a nontrivial discrete equivalence transformation. Additionally, we carry out Lie reductions of the equations under consideration up to the point equivalence, exhaustively study their hidden Lie symmetries, and generate wider families of their new exact solutions via acting by their recursion operators on constructed Lie-invariant solutions. This analysis reveals eight powers of the space variable with exponents <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$-1$</annotation>\u0000 </semantics></math>, 0, 1, 2, 3, 4, 5, and 6 as values of the diffusion coefficient that are prominent due to symmetry properties of the corresponding equations.</div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"155 3","pages":""},"PeriodicalIF":2.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145062733","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

Periodic Solutions for the Semilinear Euler–Bernoulli Beam Equation With Hinged and Elastically Fixed Ends 具有铰端和弹性固定端的半线性Euler-Bernoulli梁方程的周期解

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-15 DOI: 10.1111/sapm.70110

Qiang Sheng, Igor A. Rudakov, Shuguan Ji

引用次数: 0

Some Properties of Zeros of the Umemura Polynomials of the Fifth Painlevé Equation 第五阶painlevw方程Umemura多项式零点的一些性质

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70109

Tetsu Masuda

引用次数: 0

Nonsymmetric Askey–Wilson Shift Operators 非对称Askey-Wilson移位算子

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70102

Max van Horssen, Philip Schlösser

{"title":"Nonsymmetric Askey–Wilson Shift Operators","authors":"Max van Horssen, Philip Schlösser","doi":"10.1111/sapm.70102","DOIUrl":"https://doi.org/10.1111/sapm.70102","url":null,"abstract":"We classify the shift operators for the symmetric Askey–Wilson polynomials and construct shift operators for the nonsymmetric Askey–Wilson polynomials using two decompositions of nonsymmetric Askey–Wilson polynomials in terms of symmetric ones. These shift operators are difference–reflection operators, and we discuss the conditions under which they restrict to shift operators for the symmetric Askey–Wilson polynomials. We use them to compute the norms of the nonsymmetric Askey–Wilson polynomials and compute their specializations for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 <mo>→</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$qrightarrow 1$</annotation>\u0000 </semantics></math>. These turn out to be shift operators for the nonsymmetric Heckman–Opdam polynomials of type <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <msub>\u0000 <mi>C</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$BC_1$</annotation>\u0000 </semantics></math> that have recently been found.","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.70102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022157","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

Riemann–Hilbert Approach for the Hirota–Satsuma Coupled KdV System Hirota-Satsuma耦合KdV系统的Riemann-Hilbert方法

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70113

Haibing Zhang, Xianguo Geng, Huan Liu

{"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 In this paper, the Riemann–Hilbert (RH) method is developed to solve the Hirota–Satsuma coupled KdV (HScKdV) system associated with <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 <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.</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}

引用次数: 0

Correction to “Detecting (the Absence of) Species Interactions in Microbial Ecological Systems” 更正“在微生物生态系统中检测（不存在）物种相互作用”

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70107

引用次数: 0

On Standing Waves of 1D Nonlinear Schrödinger Equation With Triple Power Nonlinearity 具有三次非线性的一维非线性Schrödinger方程驻波

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70106

Theo Morrison, Tai-Peng Tsai

引用次数: 0

Stochastic Multisymplectic PDEs and Their Structure-Preserving Numerical Methods 随机多辛偏微分方程及其保结构数值方法

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70112

Ruiao Hu, Linyu Peng

{"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":"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.","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}

引用次数: 0

The Integrable Semi-Discrete Nonlinear Schrödinger Equations With Nonzero Backgrounds: Bilinearization-Reduction Approach 具有非零背景的可积半离散非线性Schrödinger方程：双线性化-约简方法

IF 2.3 2区数学

Studies in Applied Mathematics Pub Date : 2025-09-10 DOI: 10.1111/sapm.70108

Xiao Deng, Kui Chen, Hongyang Chen, Da-jun Zhang

引用次数: 0