Dynamic behaviors of bright and dark rogue waves for the (2+1) dimensional Nizhnik–Novikov–Veselov equation

Abstract

This paper investigates the real (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Using the Hirota trilinear form and the Taylor expansion method, the rational rogue wave is constructed. The complicated structures of rogue wave—including bright rogue wave, four-lump type rogue wave, and dark rogue wave—are presented. The existence conditions of bright and dark rogue waves are given. The dynamic behaviors of rogue waves are discussed mathematically and graphically. These results demonstrate the diversity of the structures of the rational rogue wave to the real system. It is hoped that these results may be useful for explaining some related nonlinear phenomena.