Multi-soliton, breathers, lumps and interaction solution to the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation

Abstract

In this work, we consider a (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation, which has applications in processes of interaction of exponentially localized structures. Based on the bilinear formalism and with the aid of symbolic computation, we determine multi-solitons, breather solutions, lump soliton, lump-kink waves and multi lumps using various ansatze's function. We notice that multi-lumps in the form of breathers visualize as a straight line. To realize dynamics, we commit diverse graphical analysis on the presented solutions. Obtained solutions are reliable in the mathematical physics and engineering.

Dynamical interactions between higher-order rogue waves and various forms of n-soliton solutions (n → ∞) of the (2+1)-dimensional ANNV equation

“…Let us consider the (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation [27][28][29]…”

“…[3,23] In this work, we present new theories with proper examples to built dynamical interactions between rogue waves and different forms of n-solitons solutions for the (2+1)dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation via the Hirota bilinear scheme. [24][25][26][27][28] To our knowledge, this is a first step to study these type of dynamical interactions with the existing theories for the ANNV model.…”

Interactions of rogue and solitary wave solutions to the (2 + 1)-D generalized Camassa–Holm–KP equation

“…Additional integral forms that preserve lump wave solutions are Boussinesq [21], BKP [22], Davey-Stewartson II [23], Ishimori-I [24] model equations. Due to coherent rationale results, lump propagation are analytical rational function solutions confined to a small area in every routes in space whereas lump waves are limited to a small area in nearly every but not every routes in space [25][26][27][28]. Rogue waves are bizarrely massive, erratic even rapidly occurring surface waves which can be immensely hazardous to hits the ships in deep ocean, even invert it due to massive ones.…”

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models

“…Thereupon, divergent skills have been implemented to find out multi-soliton solutions and interact soliton of nonlinear evolution equations, such as bilinear formalism and various ansatze's function [20] , novel transformation method [21] , direct rational exponential scheme [22] and multi expansion function method [23] etc. To establish the interaction and multi-soliton solution via Hirota's bilinear method, different ansatze functions was used in [24] , [25] , [26] , [27] , [28] .…”