Darboux and Bäcklund transformations approaches of the modified Camassa-Holm equation

IF 1.4 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2025-07-18 DOI:10.1007/s11005-025-01973-6

Xiaoxing Niu, Q. P. Liu, Nianhua Li

引用次数: 0

Abstract

Both the Darboux transformation (DT) and Bäcklund transformation (BT) approaches of the modified Camassa-Holm (mCH) equation are restudied. The N-DT is constructed for the mCH equation in a simple and direct way. By extending the existing 1-BT and 2-BT, the N-BT of the mCH equation is obtained. It is argued that two multi-soliton solution formulae resulted from N-DT and N-BT are equivalent. Furthermore, the DT method is applied to calulate some explicit solutions which include a solution expressed in terms of trigonometric functions.

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修正Camassa-Holm方程的Darboux和Bäcklund变换方法

重新研究了修正Camassa-Holm （mCH）方程的Darboux变换（DT）和Bäcklund变换（BT）方法。用一种简单直接的方法构造了mCH方程的N-DT。通过对已有的1-BT和2-BT的推广，得到了mCH方程的N-BT。证明了由N-DT和N-BT得到的两个多孤子解公式是等价的。此外，应用DT方法计算了一些显式解，其中包括用三角函数表示的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

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