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Journal of Vibration Testing and System Dynamics 7(2) (2023) 129--140 | DOI:10.5890/JVTSD.2023.06.002

Nail Ibragimoiv, Ranis N. Ibragimov

Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 70, Karlskrona, Sweden

Department of Mathematics, Wenatchee Valley College, WA, 98801, USA

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Abstract

A new class of exact solutions of the non-linear two-dimensional Boussinesq model for internal gravity waves is derived in this paper. The most general forms of invariant solutions, which can not be guessed from the anisotropic property and correspondingly were not reported in previous studies, are presented in this paper by infinite-dimensional Lie algebra spanned by the infinitesimal symmetries. As a particular example, it is shown here that the nonlinear two-dimensional boussinesq model for internal gravity waves is invariant with respect to the dilations and rotation symmetries that provide the class of exact solutions that has not been reported in previous studies. The new remarkable property of spinning phenomena is observed for internal waves, which has not been reported in the previous studies. The effect of nonlinearity and the earth rotation on the spinining phenomena has been studied both numerically and analytically.

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