A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions

CHEN Liguo; YANG  Liangui

doi:10.21656/1000-0887.400067

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CHEN Liguo, YANG Liangui. A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions[J]. Applied Mathematics and Mechanics, 2020, 41(1): 98-106. doi: 10.21656/1000-0887.400067

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A Nonlinear Boussinesq Equation With External Source and Dissipation Forcing Under Generalized β Plane Approximation and Its Solitary Wave Solutions

doi: 10.21656/1000-0887.400067

CHEN Liguo^1,2,
YANG Liangui¹

¹School of Mathematical Sciences, Inner Mongolia University,Hohhot 010021, P.R.China;²School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, P.R.China

Funds: The National Natural Science Foundation of China(11762011)

Received Date: 2019-02-27
Rev Recd Date: 2019-03-14
Publish Date: 2020-01-01

Abstract

Abstract

Under generalized β plane approximation, based on the quasigeostrophic potential vorticity equation, and by means of the Gardner-Morikawa transform and the weak nonlinear perturbation expansion method, a Boussinesq equation with external source and dissipation forcing was derived to describe the generation and evolution of the Rossby wave amplitude. The periodic wave solutions and solitary wave solutions for the Boussinesq equation were presented with the modified Jacobi elliptic function expansion method. The solution structure shows that, the generalized β effect, the shear basic flow, the external source and the dissipation are extremely important factors influencing the nonlinear Rossby wave.
- Boussinesq equation,
- nonlinear Rossby wave,
- Jacobi elliptic function,
- external source,
- dissipation

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References(34)

References

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