A Study on Lump Solutions to a Generalized Hirota‐Satsuma‐Ito Equation in (2+1)‐Dimensions

Abstract

The Hirota-Satsuma-Ito equation in (2+1)-dimensions passes the three-soliton test. This paper aims to generalize this equation to a new one which still has abundant interesting solution structures. Based on the Hirota bilinear formulation, a symbolic computation with a new class of Hirota-Satsuma-Ito type equations involving general second-order derivative terms is conducted to require having lump solutions. Explicit expressions for lump solutions are successfully presented in terms of coefficients in a generalized Hirota-Satsuma-Ito equation. Three-dimensional plots and contour plots of a special presented lump solution are made to shed light on the characteristic of the resulting lump solutions.

Long-Time Asymptotics of a Three-Component Coupled mKdV System

“…About coupled mKdV equations, there are many other studies such as integrable couplings [64], super hierarchies [65] and fractional analogous equations [66,67], and an important topic for further study is long-time asymptotics of those generalized integrable counterparts via the nonlinear steepest descent method. It is hoped that our result could be helpful in computing limiting behaviors of solutions incorporating features of other exact solutions, such as lumps [68,69], from the perspective of steepest descent based on RH problems.…”

Generalized nonisospectral super integrable hierarchies

“…whereĀ ,C ,D , andF (1 ≤ ≤ n), which can be showed by the potentialū and its any order derivatives of x, are undetermined items. Third, on the one hand, if we assume that t = 0 andB 0 = n in Equation 43, we obtain…”

Soliton, breather, lump and their interaction solutions of the ($2+1$)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation

“…In Refs. [34,35], some lump solutions and interaction solutions of Hirota-Satsuma-Ito equation are computed via Hirota's bilinear form through conducting symbolic computations. In Ref.…”