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. 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 that the all-defocusing type Manakov model admits bright-bright soliton solutions. Furthermore, we find that the all-defocusing type Manakov model admits bright-bright-bright soliton solutions. Therefrom, 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 for studying physical properties of the equation in Rossby waves.
Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 12102205 and 12161065), the Scientific Research Ability of Youth Teachers of Inner Mongolia Agricultural University (Grant Nos. JC2021001 and BR220126), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2022QN01003), and the Research Program of Inner Mongolia Autonomous Region Education Department (Grant Nos. NJYT23099 and NMGIRT2208).
Li-Yang Xu(徐丽阳), Xiao-Jun Yin(尹晓军), Na Cao(曹娜) and Shu-Ting Bai(白淑婷) Soliton propagation for a coupled Schrödinger equation describing Rossby waves 2023 Chin. Phys. B 32 070202
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