Variable-coefficient extended mapping method for nonlinear evolution equations

In this Letter, a variable-coefficient extended mapping method is proposed to seek new and more general exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients and (2+12+1)-dimensional Nizhnik–Novikov–Veselov equations. As a result, many new and more general exact solutions are obtained including Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics.