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

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.

Keywords

• Ostrovsky equation
• Topographic forcing
• Symmetries
• Conservation law
• Exact solutions
• Invariant solution