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arXiv · 1112.0633

Description of Nonlinear Phenomena in the Atmospheric Dynamics through Linear Wave type Equations

Rodica Cimpoiasu·Radu Constantinescu
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Abstract

The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential equations in (1+1)-dimensions which generalizes the differential equation describing the equatorial trapped waves generated in a continuously stratified ocean. This class will be obtained following the Lie symmetry and similarity reduction procedures. As a result, some concrete nonlinear second order differential equations will be proposed as possible candidates for replacing more complicated, nonintegrable systems, as the Rossby type equation. Keywords: Nonlinear dynamical systems, Lie symmetries, Similarity reduction procedure, Rossby type symmetries.

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Rodica Cimpoiasu, Radu Constantinescu. 2011-12-03. Description of Nonlinear Phenomena in the Atmospheric Dynamics through Linear Wave type Equations. https://arxiv.org/abs/1112.0633

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