Inverse scattering method and vector higher order non-linear Schrodinger equation

A generalized inverse scattering method has been developed for arbitrary n-dimensional Lax equations. Subsequently, the method has been used to obtain N-soliton solutions of a vector higher order non-linear Schrodinger equation, proposed by us. It has been shown that under a suitable reduction, the vector higher order non-linear Schrodinger equation reduces to the higher order non-linear Schrodinger equation. An infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equations. Gauge equivalence is shown between the vector higher order non-linear Schrodinger equation and the generalized Landau-Lifshitz equation and the Lax pair for the latter equation has also been constructed in terms of the spin field, establishing direct integrability of the spin system. (C) 1999 Elsevier Science B.V. All rights reserved.