On the Backlund-gauge transformation and homoclinic orbits of a coupled nonlinear Schrodinger system

The Backlund-gauge transformation for a system of coupled NLS (nonlinear Sc hrodinger) equations with a degenerate associated spectral operator is deri ved from an algebraic perspective, extending aspects of other results [M. B oiti,Tu. Guizhang, Il Nuovo Cimento 71B (1982) 253-264; D.H. Sattinger, V.D . Zurkowski, Physica D 26 (1-3) (1987) 225-250] that apply in the context o f non-degenerate spectral operators. Moreover, we demonstrate how the Backl und-gauge transformation can be used to explicitly construct the entire uns table manifold (via superpositions of homoclinic orbits) of a plane wave so lution with both self-phase instabilities and coupling instabilities. This work builds on the results of Ercolani et al. [N. Ercolani, M.G. Forest, D. W. McLaughlin, Physica D 18 (1986) 472-474; N. Ercolani, M.G. Forest, D.W. McLaughlin, Physica D 43 (2-3) (1990) 349-384] for the sine-Gordon equation , and Forest et al. [M.G. Forest, D.W. McLaughlin, D.J. Muraki, O.C. Wright , J. Nonlinear Sci., in press. M.G. Forest, S.P. Sheu, O.C. Wright, Phys. L ett. A, in press] for the integrable coupled NLS system. (C) 2000 Elsevier Science B.V. All rights reserved.