A new general algebraic method with symbolic computation to construct new exact analytical solution for a (2 + 1)-dimensional cubic nonlinear Schrödinger equation

Based on a new general ansätz, a new general algebraic method named improved Riccati equation rational expansion method is devised for constructing multiple nontravelling wave solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. With the aid of symbolic computation, we choose the (2 + 1)-dimensional cubic nonlinear Schrödinger equation to illustrate the method. As a result, six families of new exact analytical solutions for this equation are found, which include some new and more general exact rational form soliton-like solutions and triangular periodic-like solutions.