Line-rogue waves, transformed nonlinear waves and their interactions for a (3+1)-dimensional Korteweg-de Vries equation in a fluid

Abstract

Nonlinear phenomena are studied in such disciplines as meteorology, engineering, oceanography and astrophysics. In this Letter, we study a (3+1)-dimensional Korteweg-de Vries equation in a fluid. By virtue of the long-wave-limit method, the higher-order rational solutions are given. Based on the first-order rational solutions, we convert a lump into a line-rogue wave under certain condition. We investigate the effects of the coefficients in the equation for the velocities and amplitudes on the lump and line-rogue wave. Interactions between two line-rogue waves/one lump and one line-rogue wave are worked out with the second-order rational solutions. Through the characteristic-line analysis, we convert the breathers into five different types of the transformed nonlinear waves. Based on certain semi-rational solutions, interactions between the line-rogue wave and soliton/breather/transformed nonlinear wave are graphically illustrated.