Dynamics of the rogue lump in the asymmetric Nizhnik–Novikov–Veselov system

Abstract

AbstractThe (2 + 1)‐dimensional asymmetric Nizhnik–Novikov–Veselov (ANNV) equation describes an incompressible fluid such as waves with weakly nonlinear restoring forces, long internal waves in a density‐stratified ocean, or acoustic waves on a crystal lattice. In this paper, we construct a new kind of solutions doubly localized in both time and space, that is, a rogue lump wave, of the ANNV equation using the binary Darboux transformation (BDT). This solution is expressed by a class of semirational functions, in which lumps appear from one line soliton and then rapidly disappear into another line soliton. Phase parameter newly introduced in eigenfunctions plays a vital role in controlling the distinct dynamical behaviors of these rogue lumps. The explicit formulas of the approximate locations and heights of rogue waves, lumps, and line solitons are given by asymptotic analysis. Their collision process is discussed in detail. These results further help us to understand the extreme and transient waves in a variety of physical systems.