Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1999-04-29
Nonlinear Sciences
Exactly Solvable and Integrable Systems
28 pages
Scientific paper
10.1016/S0550-3213(99)00484-8
A generalised 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 nonlinear Schrodinger equation, proposed by us. It has been shown that under suitable reduction, vector higher order nonlinear Schrodinger equation reduces to higher order nonlinear Schrodinger equation. The infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equation. A gauge equivalence is shown between the vector higher order nonlinear 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.
Ghosh Sasanka
Nandy Sudipta
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