Local and nonlocal $(2+1)$-dimensional Maccari systems and their soliton solutions

TL;DR

This paper derives explicit one- and two-soliton solutions for a $(2+1)$-dimensional 3-component Maccari system using Hirota's method, including local and nonlocal reductions, and visualizes these solutions.

Contribution

It provides new integrable local and nonlocal reduced Maccari systems along with their explicit soliton solutions.

Findings

Explicit one- and two-soliton solutions for the 3-component Maccari system.

Representation of all local and Ablowitz-Musslimani type nonlocal reductions.

Visualization of soliton solutions for specific parameter values.

Abstract

In this work, by using the Hirota bilinear method, we obtain one- and two-soliton solutions of integrable $(2+1)$-dimensional $3$-component Maccari system which is used as a model describing isolated waves localized in a very small part of space and related to very well-known systems like nonlinear Schr\"{o}dinger, Fokas, and long wave resonance systems. We represent all local and Ablowitz-Musslimani type nonlocal reductions of this system and obtain new integrable systems. By the help of reduction formulas and soliton solutions of the $3$-component Maccari system, we obtain one- and two-soliton solutions of these new integrable local and nonlocal reduced $2$-component Maccari systems. We also illustrate our solutions by plotting their graphs for particular values of the parameters.