This paper is concerned with the modified Camassa–Holm equation and its Bäcklund transformation. With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent and independent variables, is constructed for the modified Camassa–Holm equation. The related nonlinear superposition formula is worked out and applications of both Bäcklund transformation and nonlinear superposition formula are considered.

中文翻译：

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改进的Camassa–Holm方程：Bäcklund变换和非线性叠加公式

本文涉及修正的Camassa–Holm方程及其Bäcklund变换。借助于倒数变换和相关的改进的Camassa-Holm方程，为改进的Camassa-Holm方程构造了一个包含因变量和自变量的Bäcklund变换。提出了相关的非线性叠加公式，并考虑了Bäcklund变换和非线性叠加公式的应用。