Soliton solutions of some nonlinear evolution equations with time-dependent coefficients

摘要

In this paper, we obtain exact soliton solutions of the modified KdV equation, inho-mogeneous nonlinear Schr??dinger equation and e??o(e?‘?, e?‘?) equation with variable coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation are also given.