Construction of 2-peakon solutions and nonuniqueness for a generalized mCH equation
Summary: For the generalized mCH equation, we construct a 2-peakon solution on both the line and the circle, and we can control the size of the initial data. The two peaks at different speeds move in the same direction and eventually collide. This phenomenon is that the solution at the collision time is consistent with another solitary peakon solution. By reversing the time, we get two new solutions with the same initial value and different values at the rest of the time, which means the nonuniqueness for the equation in Sobolev spaces \(H^s\) is proved for \(s<3/2\).
generalized mCH equation on the line or the circle
scientific article; zbMATH DE number 7452866
scientific article