Solitary and periodic wave solutions of the Majda–Biello system

Abstract

In this paper, we present the exact solutions of the Majda–Biello system. This system describes the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a substantial midlatitude projection, in the presence of suitable horizontally and vertically sheared zonal mean flows. The methods used to construct the exact solutions are the Kudryashov method and Jacobi elliptic function method. These two methods yield solitary wave solutions and periodic wave solutions.