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

Abstract

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 Schrödinger, 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.