  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.
