Multisoliton Solutions of the (3+1)-Dimensional Nizhnik–Novikov–Veselov Equation**The project supported by Outstanding Youth Foundation, Research Fund for the Doctoral Program of Higher Education of China and National Natural Science Foundation of China

Abstract

Using the standard truncated Painlevé analysis, we can obtain a Bäcklund transformation of the (3+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation and get some (3+1)-dimensional single-, two- and three-soliton solutions and some new types of multisoliton solutions of the (3+1)-dimensional NNV system from the Bäcklund transformation and the trivial vacuum solution.