Abstract

We describe an approach that allows us to construct multi-soliton asymptotic solutions for essentially nonintegrable equations and analyze the type of wave collision. The general idea is demonstrated by the example of a generalization of Korteweg-de Vries equation with small dispersion in the cases of two and three waves. We also discuss the phenomenon of nonuniqueness that occurs in the framework of the weak description of a multi-soliton interaction.

中文翻译：

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不可积分方程的弱多相渐近性

摘要

我们描述了一种方法，该方法使我们能够为基本不可积分的方程构造多孤子渐近解并分析波碰撞的类型。通过对两波和三波情况下色散较小的Korteweg-de Vries方程进行推广，可以证明这一总体思想。我们还讨论了在多孤子相互作用的弱描述框架内发生的非唯一性现象。