Symmetries, conservation laws, and generalized travelling waves for a forced Ostrovsky equation

TL;DR

This paper analyzes a forced Ostrovsky equation modeling long waves in rotating fluids with variable topography, classifies its symmetries and conservation laws, and derives generalized traveling wave solutions with diverse wave profiles.

Contribution

It provides a comprehensive symmetry classification and constructs generalized traveling wave solutions for the forced Ostrovsky equation, extending previous analyses.

Findings

Classification of Lie point symmetries and conservation laws.

Derivation of generalized traveling wave solutions with variable speeds.

Wave profiles stationary in moving reference frames with different accelerations.

Abstract

Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation laws is presented. Generalized travelling wave solutions are obtained through symmetry reduction. These solutions exhibit a wave profile that is stationary in a moving reference frame whose speed can be constant, accelerating, or decelerating.