Riemann–Hilbert problem for a (3+1)-dimensional nonlinear evolution equation

Abstract

This paper concentrates on a (3+1)-dimensional nonlinear evolution equation. By introducing a transformation, the (3+1)-dimensional nonlinear evolution equation is decomposed into three integrable (1+1)-dimensional models. On the basis of a quartet Lax pair, we build the associated matrix Riemann–Hilbert problem. As a consequence, solving the obtained matrix Riemann–Hilbert problem with the identity jump matrix, corresponding to the reflectionless, the soliton solution to the (3+1)-dimensional nonlinear evolution equation is acquired. Specially, the one-soliton solutions are worked out and analyzed graphically.