Lump and Stripe Soliton Solutions to the Generalized Nizhnik-Novikov-Veselov Equation

Abstract

With the aid of the truncated Painlevé expansion, a set of rational solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation with the quadratic function which contains one lump soliton is derived. By combining this quadratic function and an exponential function, the fusion and fission phenomena occur between one lump soliton and a stripe soliton which are two kinds of typical local excitations. Furthermore, by adding a corresponding inverse exponential function to the above function, we can derive the solution with interaction between one lump soliton and a pair of stripe solitons. The dynamical behaviors of such local solutions are depicted by choosing some appropriate parameters.

Lump and Mixed Rogue‐Soliton Solutions of the (2 + 1)‐Dimensional Mel’nikov System

“…Many methods are very powerful to investigate the nonlinear evolution equations, such as the Darboux transformation [2,6], the inverse scattering transformation [1,7], and the Hirota bilinear method [8,9]. Recently, lump waves, rogue waves, and the interaction solutions between the lump and soliton have intensively aroused much attention [10][11][12][13][14][15][16][17].…”

Evolution and emergence of new lump and interaction solutions to the (2+1)-dimensional Nizhnik–Novikov–Veselov system

“…Wang et al reported its bright and dark rogue waves by applying Hirota's trilinear method [43]. Ma et al discussed its lump solutions, stripe soliton, and interaction solutions by applying the direct method [44].…”