Dynamics of mixed lump-soliton for an extended (2+1)-dimensional asymmetric Nizhnik–Novikov–Veselov equation

Abstract

A new (2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov (eANNV) equation is proposed by introducing the additional bilinear terms to the usual ANNV equation. Based on the independent transformation, the bilinear form of the eANNV equation is constructed. Lump wave is guaranteed by introducing a positive constant term in the quadratic function. In the meanwhile, different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions. For interaction between lump wave and one-soliton, the energy of lump wave and one-soliton can transfer each other at different time. The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term. The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional, contour and density plots.

Breather, lump, and interaction solutions to a nonlocal KP system

“…Since most of the nonlinear PDEs of physically significant are written in high dimensions, whether these equations can be integrated is a question of fundamental importance. Shi et al obtained mixed lump-soliton solutions for the extended highdimensional Nizhnik-Novikov-Veselov equation using the Hirota bilinear method [31]. Wei et al derived soliton molecules and multi-breather solutions for the high-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani equation [32].…”