On a homoclinic manifold of a coupled long-wave–short-wave system

A Bäcklund transformation is obtained for linearly unstable spatially independent plane-wave solutions of a system of coupled long-wave–short-wave resonance equations. Explicit expressions are constructed for the periodic orbits lying on a homoclinic manifold of a torus of planewaves by evaluating the Bäcklund transformation at double points of an irreducible factor of the Floquet spectral curve of the associated scattering problem.