Integrability of the η-deformed Neumann–Rosochatius model

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An integrable deformation of the well-known Neumann–Rosochatius system is studied by considering generalised bosonic spinning solutions on the η-deformed background. For this integrable model we construct a Lax representation and a set of integrals of motion that ensures its Liouville integrability. These integrals of motion correspond to the deformed analogues of the Neumann–Rosochatius integrals and generalise the previously found integrals for the η-deformed Neumann and geodesic systems. Finally, we briefly comment on consistent truncations of this model.