Abstract: In this paper, a variable-coefficient simplest equation method is proposed to establish exact solutions for nonlinear evolution equations. For illustrating the validity of this method, we apply it to the asymmetric (2+1)-dimensional NNV system, the (2+1)-dimensional dispersive long wave equations and the (2+1)-dimensional Boussinesq and Kadomtsev-Petviashvili equations. As a result, some new exact solutions and solitary wave solutions involving arbitrary function as coefficients are obtained for them.
DOI: *As the DOI is a unique identifier, it is already available in the pdf version. **The DOI link will be activated in the first midst of January 2026.