Soliton propagation for a coupled Schrödinger equation describing Rossby waves

Abstract

Abstract We study a coupled Schrödinger equation which is started from the Boussinesq equation of atmospheric gravity waves by using multiscale analysis and reduced perturbation method in this paper. For the coupled Schrödinger equation, we obtain the Manakov model of all-focusing, all-defocusing and mixed types by setting parameters value and apply the Hirota bilinear approach to provide the two-soliton and three-soliton solutions. Especially, we find the all-defocusing type Manakov model admits bright-bright soliton solutions, what’s more, we find the all-defocusing type Manakov model admits bright-bright-bright soliton solutions. Following that, we go over how the free parameters affect the Manakov model’s all-focusing type’s two-soliton and three-soliton solutions’ collision locations, propagation directions, and wave amplitudes. These findings are useful for setting a simulation scene in Rossby waves research. The answers we have found are helpful to study the equation’s physical properties in Rossby waves.