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

Abstract EN

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.