Hamiltonian formulation, nonintegrability and local bifurcations for the Ostrovsky equation

TL;DR

This paper investigates the Ostrovsky equation, demonstrating its nonintegrability and analyzing local bifurcations of solitary waves within a Hamiltonian framework, contributing to the understanding of gravity wave models.

Contribution

It proves the nonintegrability of the Ostrovsky equation and studies the local bifurcations of its solitary waves, expanding knowledge of its dynamical properties.

Findings

Proved the Ostrovsky equation is nonintegrable.

Analyzed local bifurcations of solitary waves.

Enhanced understanding of gravity wave dynamics.

Abstract

The Ostrovsky equation is a model for gravity waves propagating down a channel under the influence of Coriolis force. This equation is a modification of the famous Korteweg-de Vries equation and is also Hamiltonian. However the Ostrovsky equation is not integrable and in this contribution we prove its nonintegrability. We also study local bifurcations of its solitary waves.