Blow-up solution near the traveling waves for the second-order Camassa–Holm equation. (April 2021) - Ding, Danping; Wang, Kai
Abstract: 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. Highlights: The sufficient condition for the existence of blow-up solution. Extended pseudo-conformal transformation. An equivalent proposition of the solution breaking in finite time. The relation between the blow-up time and rate of the solution and residual's.