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

We propose a systematic method for generalizing the integrable Rosochatius deformations for finite-dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite-dimensional integrable equations. An infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable Henon-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.