New quasi-periodic waves and theirs interactions in (2 + 1)-dimensional nonlinear systems

In this study the general variable separated approach is successfully extended to the (2 + 1)-dimensional physical model. An universal formula involving arbitrary number of variable separated functions is obtained. Because of the existence of the arbitrary functions in the universal formula, new exact quasi-periodic and non-periodic solutions for the (2 + 1)-dimensional nonlinear systems are demonstrated both analytically and graphically by means of the Jacobi elliptic functions with the space–time-dependent modulus. Some novel features or interesting behaviors are revealed.