双曲单峰奇点确定的积分渐近线的重构

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-12-01 DOI:10.1134/s0016266323040056

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引用次数: 0

摘要

摘要研究了指数积分的渐近行为，其中相位函数的形式是类型为 \(T_{4,4,4}\) 的双曲单峰奇点的胚芽的特殊变形。所研究的积分满足热方程，其科尔-霍普夫变换给出了四维时空中矢量布尔格斯方程的解，其主要渐近近似值用三级代数方程系统的实解表示。所获得的分析结果使我们有可能根据奇点模数参数追踪渐近结构的分岔。

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Reconstructions of the Asymptotics of an Integral Determined by a Hyperbolic Unimodal Singularity

Abstract

The asymptotic behavior of an exponential integral is studied in which the phase function has the form of a special deformation of the germ of a hyperbolic unimodal singularity of type \(T_{4,4,4}\) . The integral under examination satisfies the heat equation, its Cole–Hopf transformation gives a solution of the vector Burgers equation in four-dimensional space-time, and its principal asymptotic approximations are expressed in terms of real solutions of systems of third-degree algebraic equations. The obtained analytical results make it possible to trace the bifurcations of an asymptotic structure depending on the parameter of the modulus of the singularity.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.