A New Class of Separable Lagrangian Systems Generalizing Sawada–Kotera System

Abstract

Some characteristics of stationary flows of the Sawada–Kotera system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom. All of these systems come in couples that have the same equations of motion, although they are not related by a gauge transform. Some nonpolynomial examples are provided.

Keywords

• integrable systems
• separation of coordinates
• generalized Hénon–Heiles systems