Physikalische Mathematik

New Exact Solutions for the Maccari System

Abstract

Abdelrahman MAE and Hassan SZ

In this article we apply three mathematical methods for solving the Maccari system, namely, the exp(-ϕ(ξ))- expansion method, the sine-cosine approach and the Riccati-Bernoulli sub-ODE method. These methods are used to construct new and general exact periodic and soliton solutions of the Maccari system. This nonlinear system can be turned into another nonlinear ordinary differential equation by suitable transformation. It is shown that the exp(-ϕ(ξ))-expansion method, the sine-cosine method and the Riccati-Bernoulli sub-ODE method provide a powerful mathematical tool for solving a great many systems of nonlinear partial differential equations in mathematical physics.