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

TL;DR

This paper introduces a method to extend linear wave equations to nonlinear models in atmospheric dynamics, using Lie symmetries and similarity reductions, to better understand phenomena like equatorial trapped waves.

Contribution

It presents a systematic approach to generate nonlinear differential equations from linear wave equations, aiding the modeling of complex atmospheric phenomena.

Findings

Derived a class of nonlinear second order differential equations

Proposed candidates to replace complex nonintegrable systems

Applied Lie symmetry and similarity reduction techniques

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.