{"title":"Systems of Differential Equations for Determining the Fundamental Vector of Special Wave Catastrophes","authors":"A.S. Kryukovsky, D.S. Lukin, D.V. Rastyagaev","doi":"10.1134/S1061920824040083","DOIUrl":null,"url":null,"abstract":"<p> Uniform asymptotic solutions of the field structures in the vicinity of focusing based on the use of the Maslov canonical operator leads to investigation of special functions of wave catastrophe (SWC) and their first derivatives. The method for constructing a system of differential equations to determine the fundamental vector of special functions of wave catastrophes (SWC) is created. This approach allows us to reduce the solution of the problem of determining the SWCs and their derivatives to the solution of the Cauchy problem for a system of ordinary differential equations. The paper provides examples of the construction of such systems for special functions of edge catastrophes corresponding to Lagrange manifolds with boundary and special functions of main catastrophes corresponding to Lagrange manifolds without restrictions. </p><p> <b> DOI</b> 10.1134/S1061920824040083 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 4","pages":"691 - 705"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920824040083","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Uniform asymptotic solutions of the field structures in the vicinity of focusing based on the use of the Maslov canonical operator leads to investigation of special functions of wave catastrophe (SWC) and their first derivatives. The method for constructing a system of differential equations to determine the fundamental vector of special functions of wave catastrophes (SWC) is created. This approach allows us to reduce the solution of the problem of determining the SWCs and their derivatives to the solution of the Cauchy problem for a system of ordinary differential equations. The paper provides examples of the construction of such systems for special functions of edge catastrophes corresponding to Lagrange manifolds with boundary and special functions of main catastrophes corresponding to Lagrange manifolds without restrictions.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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