Formal initial value problem of the Korteweg-de Vries equation

被引：0

作者：

Kim, Namhoon ^{[1
]}

机构：

[1] Hongik Univ, Dept Math Educ, Seoul, South Korea

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2015年 / 48卷 / 05期

关键词：

KdV equation; formal solution; formal inverse scattering method;

D O I：

10.1088/1751-8113/48/5/055207

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the initial value problem of the Korteweg-de Vries (KdV) equation on a space of generalized formal power series. We derive an explicit expression of the solution of the KdV equation with an arbitrary initial condition, using a recursively defined sequence of rational functions. From this result one can explain the formal analogues of the direct and inverse scattering transforms, relating the given initial condition to the solution of the formal Gelfand-Levitan-Marchenko equation.

引用

页数：15

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