On a Homoclinic Manifold of a Coupled Long-wave-short-wave System
Communications in Nonlinear Science and Numerical Simulation
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.
Heteroclinic connections; Bäcklund transformation; Dressing method; Long-wave-short-wave resonance
Wright, O. C. (2010). On a homoclinic manifold of a coupled long-wave-short-wave system. Communications in Nonlinear Science and Numerical Simulation, 15, 2066-2072.