ar X iv : s ol v - in t / 9 90 40 21 v 1 2 9 A pr 1 99 9 INVERSE SCATTERING METHOD AND VECTOR HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION
نویسنده
چکیده
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 nonlinear Schrödinger equation, proposed by us. It has been shown that under suitable reduction, vector higher order nonlinear Schrödinger equation reduces to higher order nonlinear Schrödinger equation. The infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equations. A gauge equivalence is shown between the vector higher order nonlinear Schrödinger 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.
منابع مشابه
ar X iv : s ol v - in t / 9 90 40 21 v 2 3 0 A pr 1 99 9 INVERSE SCATTERING METHOD AND VECTOR HIGHER ORDER NONLINEAR SCHRÖDINGER 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 nonlinear Schrödinger equation, proposed by us. It has been shown that under suitable reduction, vector higher order nonlinear Schrödinger equation reduces to higher order nonlinear Schrödinger equatio...
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