Globally conservative solutions for the modified Camassa-Holm (MOCH) equation

In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa-Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to the standard ordinary differential equation theory with the aid of the conservation law, we give the global solutions of the semi-linear system. Finally, returning to the original variables, we obtain the globally conservative solutions to the MOCH equation.

Automated summary

This paper presents globally conservative solutions to the Cauchy problem for the modified Camassa-Holm equation by transforming the equation into an equivalent semi-linear system, giving global solutions through the standard ordinary differential equation theory and conservation law, and obtaining the solutions back in the original variables.