This paper studies the blow-up solution and its blow-up rate near the traveling waves of the second-order Camassa–Holm equation. The sufficient condition for the existence of blow-up solution is obtained by a rather ingenious method. Applying the extended pseudo-conformal transformation, an equivalent proposition of the solution breaking in finite time near the traveling waves is constructed. The relation is established between the blow-up time and rate of the solution and the residual’s.

中文翻译：

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二阶Camassa-Holm方程行波附近的爆破解

本文研究了二阶Camassa-Holm方程行波附近的爆破解及其爆破率。爆破溶液存在的充分条件是通过相当巧妙的方法获得的。应用扩展的伪保形变换，构造了行波附近有限时间内破裂的解的一个等效命题。在溶液的爆破时间，爆破时间和残渣率之间建立了关系。