7,876 research outputs found
Properties of an Alternate Lax Description of the KdV Hierarchy
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 -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
Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger Equation
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
Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras
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
Davey-Stewartson Equation from a Zero Curvature and a Self-Duality Condition
We derive the two equations of Davey-Stewartson type from a zero curvature
condition associated with SL(2,{\bf R}) in dimensions. We show in general
how a dimensional zero curvature condition can be obtained from the
self-duality condition in 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 dimensions.Comment: 9 pages, UR-1332, ER-40685-78
Supersymmetric Two Boson Equation, Its Reductions and the Nonstandard Supersymmetric KP Hierarchy
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 extended supersymmetric system.Comment: 44 pages, plain Te
Self-Duality and the KdV Hierarchy
We derive the entire KdV hierarchy as well as the recursion relations from
the self-duality condition on gauge fields in four dimensions.Comment: 7 page
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