Global existence of the solution of the modified Camassa-Holm equation with step-like boundary conditions

I. Karpenko, D. Shepelsky, G. Teschl

We consider the Cauchy problem for the modified Camassa-Holm equation \[ u_t+\left((u^2-u_x^2)m\right)_x=0,\quad m\coloneqq u-u_{xx}, \quad t>0,\ \ -\infty<x<+\infty \] subject to…