Primitive solutions of the Korteweg–de Vries equation

被引：0

作者：

S. A. Dyachenko

P. Nabelek

D. V. Zakharov

V. E. Zakharov

机构：

[1] University of Washington,Department of Mathematics

[2] Oregon State University,Department of Mathematics

[3] Central Michigan University,Department of Mathematics

[4] University of Arizona,Department of Mathematics

[5] Skolkovo Institute of Science and Technology,undefined

来源：

Theoretical and Mathematical Physics | 2020年 / 202卷

关键词：

integrable system; Korteweg-de Vries equation; primitive solution;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We survey recent results connected with constructing a new family of solutions of the Korteweg-de Vries equation, which we call primitive solutions. These solutions are constructed as limits of rapidly vanishing solutions of the Korteweg-de Vries equation as the number of solitons tends to infinity. A primitive solution is determined nonuniquely by a pair of positive functions on an interval on the imaginary axis and a function on the real axis determining the reflection coefficient. We show that elliptic one-gap solutions and, more generally, periodic finite-gap solutions are special cases of reflectionless primitive solutions.

引用

页码：334 / 343

页数：9