Journal
COMMUNICATIONS IN THEORETICAL PHYSICS
Volume 71, Issue 9, Pages 1054-1062Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0253-6102/71/9/1054
Keywords
generalized Boussinesq model equation; nonlinear Rossby waves; dynamical analysis; traveling wave solutions; nonlinear perturbation expansions; bifurcation theory of planar dynamical systems
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Funding
- National Natural Science Foundation of China [11562014, 11762011, 11671101, 71471020, 51839002]
- Natural Science Foundation of Inner Mongolia [2017MS0108]
- Hunan Provincial Natural Science Foundation of China [2016JJ2061]
- Scientific Research Fund of Hunan Provincial Education Department [18A325]
- Construct Program of the Key Discipline in Hunan Province [201176]
- Aid Program for Science and Technology Innovative Research Team in Higher Educational Instituions of Hunan Province [2014207]
- Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering of Changsha University of Science and Technology [018MMAEZD191]
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In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect. Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A 383 (2019) 514], we derive a new (2 + 1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.
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