1-Soliton solution of the D(m, n) equation with generalized evolution

This paper obtains the 1-soliton solution of the nonlinear dispersive Drinfel’d–Sokolov equation with power law nonlinearity. In the first case the soliton solution is without the generalized evolution. The solitary wave ansatz method is used to carry out the integration. Subsequently, the He’s semi-inverse variational principle is used to integrate the equation with power law nonlinearity. Parametric conditions for the existence of envelope solitons are given.