Lie symmetry analysis, optimal system and conservation law of a generalized (2+1)-dimensional Hirota-Satsuma-Ito equation

In this paper, a generalized (2+1)-dimensional Hirota-Satsuma-Ito (GHSI) equation is investigated using Lie symmetry approach. Infinitesimal generators and symmetry groups of this equation are presented, and the optimal system is given with adjoint representation. Based on the optimal system, some symmetry reductions are performed and some similarity solutions are provided, including soliton solutions and periodic solutions. With Lagrangian, it is shown that the GHSI equation is nonlinearly self-adjoint. By means of the Lie point symmetries and nonlinear self-adjointness, the conservation laws are constructed. Furthermore, some physically meaningful solutions are illustrated graphically with suitable choices of parameters.

Automated summary

This paper investigates a generalized (2+1)-dimensional Hirota-Satsuma-Ito (GHSI) equation using Lie symmetry approach. The study identifies some symmetries and similarity solutions, demonstrates the nonlinear self-adjointness of the equation, and constructs conservation laws based on Lie point symmetries and nonlinear self-adjointness. Additionally, physically meaningful solutions are illustrated graphically with appropriate parameter choices.