Nonlinearly dispersive mKdV equations and weak compactons

We are concerned with the nonlinearly dispersive mKdV (mK(m,n)) equations. The conservation laws are obtained by using the rank analysis method and the transformation relationship between conservation laws and the traveling wave ordinary differential equation (ODE) is presented. We establishes precise conditions for weak compactons based on the power the nonlinearity powers in this equation via cutoff conditions, which is different from previous studies on exact compacton solutions. Moreover, the weak compactons, formulae of compactons and pattern solutions are given.