Infinite generation of soliton-like solutions for complex nonlinear evolution differential equations via the NLSE-based constructive method

Inspired by the mapping method and the direct method of symmetry reduction, we present a nonlinear Schrödinger equation-based constructive method for solving complex nonlinear evolution equations. This method can easily generate infinite soliton-like solutions of the complex nonlinear evolution equations based on the abundant solutions of the nonlinear Schrödinger equation. These solutions include multi-soliton solutions with or without background (continuous or cnoidal wave background), rational solutions and periodic solutions. As an illustration, we apply this method to solve (3 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation and obtain multi-soliton solutions with continuous and cnoidal wave backgrounds.