Tests of integrability of the supersymmetric nonlinear Schrödinger equation | Zendy

J. C. Brunelli | Zendy; Ashok Das | Zendy

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Tests of integrability of the supersymmetric nonlinear Schrödinger equation

Author(s) -

J. C. Brunelli,

Ashok Das

Publication year - 1995

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.531370

Subject(s) - nonlinear system , nonlinear schrödinger equation , mathematical physics , schrödinger equation , physics , supersymmetry , mathematics , quantum mechanics

We apply various conventional tests of integrability to the supersymmetricnonlinear Schr\"odinger equation. We find that a matrix Lax pair exists andthat the system has the Painlev\'e property only for a particular choice of thefree parameters of the theory. We also show that the second Hamiltonianstructure generalizes to superspace only for these values of the parameters. Weare unable to construct a zero curvature formulation of the equations based onOSp(2$|$1). However, this attempt yields a nonsupersymmetric fermionicgeneralization of the nonlinear Schr\"odinger equation which appears to possessthe Painlev\'e property.Comment: 21 pages, UR-1344, ER-40685-79

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