On the coherent structures of the Nizhnik–Novikov–Veselov equation

Abstract

A variable separation approach is used to obtain exact solutions of high-dimensional nonlinear physical models. Taking the Nizhnik–Novikov–Veselov (NNV) equation as a simple example, we show that a high-dimensional nonlinear physical model may have quite rich localized coherent structures. For the NNV equation, the richness of the localized structures caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the NNV equation may be dromions, lumps, breathers, instantons and ring solitons, etc.