Solutions Classification to the Extended Reduced Ostrovsky Equation

TL;DR

This paper proposes a new qualitative approach for classifying solutions to the extended reduced Ostrovsky equation, utilizing phase plane analysis and mechanical analogies, offering a more vivid and less restricted method than previous approaches.

Contribution

It introduces an alternative, more intuitive method based on qualitative differential equations theory for categorizing solutions to the exROE, improving upon Parkes' approach.

Findings

Provides a classification framework using phase plane analysis.

Demonstrates the approach's effectiveness and clarity.

Offers insights into solution behaviors of the exROE.

Abstract

An alternative to the Parkes' approach [SIGMA 4 (2008) 053, arXiv:0806.3155] is suggested for the solutions categorization to the extended reduced Ostrovsky equation (the exROE in Parkes' terminology). The approach is based on the application of the qualitative theory of differential equations which includes a mechanical analogy with the point particle motion in a potential field, the phase plane method, analysis of homoclinic trajectories and the like. Such an approach is seemed more vivid and free of some restrictions contained in the above mentioned Parkes' paper.