ON THE METHOD OF A SMALL PARAMETER IN NONLINEAR MATHEMATICAL PHYSICS

被引：1

作者：

Kachalov, Vasiliy Ivanovich ^{[1
]}

Fedorov, Yuri Sergeevich ^{[1
]}

机构：

[1] Natl Res Univ MPEI, St Krasnokazarmennaya 14, Moscow 111250, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2018年 / 15卷

关键词：

Burgers equation; Klein-Gordon equation; analytic solution; Faa-da-Bruno formula;

D O I：

10.33048/semi.2018.15.139

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The method of a small parameter has been used in mathematical physics for a long time. However, with its help, in general, asymptotic solutions of differential equations are obtained. In the framework of the regularization method, S.A. Lomov proved that under certain restrictions on the data of the problem, one can obtain solutions in the form of series converging in the usual sense in powers of the small parameter, that is, solutions analytically dependent on the parameter. Here we consider two equations - the Burgers equation and the Klein-Gordon equation. The first of them represents a one-dimensional model of hydrodynamics, and the second one is considered in quantum field theory.

引用

页码：1680 / 1686

页数：7

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