Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources

TL;DR

This paper introduces a systematic approach to extend integrable Rosochatius deformations from finite to infinite dimensional systems, applying it to various soliton hierarchies with self-consistent sources and providing their Lax representations.

Contribution

It develops a general method for infinite-dimensional integrable Rosochatius deformations and applies it to multiple soliton hierarchies, including KdV, AKNS, and mKdV with self-consistent sources.

Findings

Constructed infinite integrable Rosochatius deformations for soliton hierarchies.

Derived Lax representations for the deformed hierarchies.

Included deformations of the generalized Hénon-Heiles system.

Abstract

We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable H$\acute{e}$non-Heiles system, and the integrable Rosochatius deformations of the KdV hierarchy with self-consistent sources, of the AKNS hierarchy with self-consistent sources and of the mKdV hierarchy with self-consistent sources as well as their Lax representations are presented.