Searcharxiv⌕ Search

arXiv subjects

J. C. Brunelli

Publications and source records attributed to J. C. Brunelli.

28 records · Page 2Linked to original sources
arXiv1995

Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger Equation

We show that the supersymmetric nonlinear Schrödinger 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.

hep-th↗
arXiv1995

Properties of Nonlocal Charges in the Supersymmetric Two Boson Hierarchy

We obtain the conserved, nonlocal charges for the supersymmetric two boson hierarchy from fractional powers of its Lax operator. We show that these charges reduce to the ones of the supersymmetric KdV system under appropriate reduction. We study the algebra of the nonlocal, local and supersymmetry charges with respect to the first and the second Hamiltonian structures of the system and discuss how they close as a graded nonlinear cubic algebra.

hep-th↗
arXiv1995

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 $n$-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.

hep-th↗
arXiv1994

KDV and NLS Equations as Tri-Hamiltonian Systems

We show that the KdV and the NLS equations are tri-Hamiltonian systems. We obtain the third Hamiltonian structure for these systems and prove Jacobi identity through the method of prolongation. The compatibility of the Hamiltonian structures is verified directly through prolongation as well as through the shifting of the variables. We comment on the properties of the recursion operator as well as the connection with the two boson hierarchy.

hep-th↗
arXiv1994

A Nonstandard Supersymmetric KP Hierarchy

We show that the supersymmetric nonlinear Schrödinger 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.

hep-th↗
arXiv1994

The Supersymmetric Two Boson Hierarchies

We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to the supersymmetric nonlinear Schrödinger equation without any arbitrary parameter which is known to be integrable. We show that this supersymmetric system has three local Hamiltonian structures just like the bosonic counterpart and we show how the supersymmetric KdV equation can be embedded into this system.

hep-th↗
arXiv1994

Tests of Integrability of the Supersymmetric Nonlinear Schrodinger Equation

We apply various conventional tests of integrability to the supersymmetric nonlinear Schrödinger equation. We find that a matrix Lax pair exists and that the system has the Painlevé property only for a particular choice of the free parameters of the theory. We also show that the second Hamiltonian structure generalizes to superspace only for these values of the parameters. We are unable to construct a zero curvature formulation of the equations based on OSp(2$|$1). However, this attempt yields a nonsupersymmetric fermionic generalization of the nonlinear Schrödinger equation which appears to possess the Painlevé property.

hep-th↗
arXiv1993

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 $2+1$ dimensions. We show in general how a $2+1$ dimensional zero curvature condition can be obtained from the self-duality condition in $3+3$ 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 $3+3$ dimensions.

hep-th↗
arXiv1993

The Algebra of Non-Local Charges in Non-Linear Sigma Models

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower.

hep-th↗