44,588 research outputs found

    Properties of an Alternate Lax Description of the KdV Hierarchy

    Get PDF
    We study systematically the Lax description of the KdV hierarchy in terms of an operator which is the geometrical recursion operator. We formulate the Lax equation for the nn-th flow, construct the Hamiltonians which lead to commuting flows. In this formulation, the recursion relation between the conserved quantities follows naturally. We give a simple and compact definition of all the Hamiltonian structures of the theory which are related through a power law.Comment: 11 pages, plain Te

    Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras

    Full text link
    We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis, further, suggests a systematic method of constructing higher dimensional representations for the zero curvature condition starting with the fundamental representation. We illustrate this with the examples of the sTB hierarchy and the sKdV hierarchy. This would be particularly useful in constructing explicit higher dimensional representations of graded Lie algebras.Comment: 13 pages, late

    Supersymmetric Two Boson Equation, Its Reductions and the Nonstandard Supersymmetric KP Hierarchy

    Get PDF
    In this paper, we review various properties of the supersymmetric Two Boson (sTB) system. We discuss the equation and its nonstandard Lax representation. We construct the local conserved charges as well as the Hamiltoniam structures of the system. We show how this system leads to various other known supersymmetric integrable models under appropriate field redefinition. We discuss the sTB and the supersymmetric nonlinear Schr\"odinger (sNLS) equations as constrained, nonstandard supersymmetric Kadomtsev-Petviashvili (sKP) systems and point out that the nonstandard sKP systems naturally unify all the KP and mKP flows while leading to a new integrable supersymmetrization of the KP equation. We construct the nonlocal conserved charges associated with the sTB system and show that the algebra of charges corresponds to a graded, cubic algebra. We also point out that the sTB system has a hidden supersymmetry making it an N=2N=2 extended supersymmetric system.Comment: 44 pages, plain Te

    Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger Equation

    Get PDF
    We show that the supersymmetric nonlinear Schr\"odinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two boson hierarchy as well.Comment: 13 pages, plain Te

    Davey-Stewartson Equation from a Zero Curvature and a Self-Duality Condition

    Full text link
    We derive the two equations of Davey-Stewartson type from a zero curvature condition associated with SL(2,{\bf R}) in 2+12+1 dimensions. We show in general how a 2+12+1 dimensional zero curvature condition can be obtained from the self-duality condition in 3+33+3 dimensions and show in particular how the Davey-Stewartson equations can be obtained from the self-duality condition associated with SL(2,{\bf R}) in 3+33+3 dimensions.Comment: 9 pages, UR-1332, ER-40685-78

    A Nonstandard Supersymmetric KP Hierarchy

    Get PDF
    We show that the supersymmetric nonlinear Schr\"odinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.Comment: 18 pages, plain TeX, UR-1367, ER-40685-81
    • …
    corecore