DARBOUX TRANSFORMATION AND VARIOUS SOLUTIONS FOR A NONLINEAR EVOLUTION EQUATION IN (3 + 1)-DIMENSIONS

A new (3 + 1)-dimensional nonlinear evolution equation can be decomposed into three (1 + 1)-dimensional nonlinear evolution equations. In this paper, N-soliton solution, resonant solution and complexiton solution of the (3 + 1)-dimensional nonlinear evolution equation are obtained via an N-fold Darboux transformation of the Ablowitz–Kaup–Newell–Segur spectral problems.