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

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