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

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