On the construction of orbits homoclinic to plane waves in integrable coupled nonlinear Schrodinger systems

Plane waves of coupled NLS PDEs are known to possess self-focusing and cros s-coupling instabilities. In the integrable limit of coupled NLS systems, t hese instabilities are accompanied by homoclinic orbits which asymptoticall y (in time) approach the unstable plane wave. Here we use the integrable me thod of Backlund transformations to construct a two-parameter family of exa ct spatially periodic CNLS solutions, which consist of a plane wave connect ed to a nonlinear superposition of self-focusing and cross-coupling homocli nic orbits. (C) 2000 Published by Elsevier Science B.V. All rights reserved .