Nonlinear dynamics of higher-order rogue waves in a novel complex nonlinear wave equation

Abstract

A novel complex nonlinear wave equation was recently found by Mukherjee and Kundu (Phys. Lett. A 383:985–990, 2019) and shown that it possesses the first-order rogue waves and accelerated one-soliton solutions. In this paper, higher-order rogue wave solutions with multi-parameters of the novel complex nonlinear wave equation are derived by a symbolic computation approach. Nonlinear dynamics of the first- and second-order rogue wave solutions, localized in space–time and richer due to the presence of free parameters, are investigated in detail. In particular, a complete classification of the first-order rogue wave is given by the free parameters. With the help of the contour line method, some localization characters of the first-order rogue wave solution are analyzed. Moreover, the novel equation also allows some periodic wave and accelerated periodic wave solutions expressed by Jacobi elliptical functions.