21,351 research outputs found
Classical Integrable N=1 and Super Sinh-Gordon Models with Jump Defects
The structure of integrable field theories in the presence of jump defects is
discussed in terms of boundary functions under the Lagrangian formalism.
Explicit examples of bosonic and fermionic theories are considered. In
particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models
are constructed and shown to generate the Backlund transformations for its
soliton solutions. As a new and interesting example, a solution with an
incoming boson and an outgoing fermion for the N=1 case is presented. The
resulting integrable models are shown to be invariant under supersymmetric
transformation.Comment: talk presented at the V International Symposium on Quantum Theory and
Symmetries, Valladolid, Spain, July 22-28,200
The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy
It is shown how the complex sine-Gordon equation arises as a symmetry flow of
the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry
flows forming the Borel loop algebra. The complex sine-Gordon and the vector
Nonlinear Schrodinger equations appear as lowest negative and second positive
flows within the extended hierarchy. This is fully analogous to the well-known
connection between the sine-Gordon and mKdV equations within the extended mKdV
hierarchy.
A general formalism for a Toda-like symmetry occupying the ``negative''
sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel
sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update
Plastic Deformation of 2D Crumpled Wires
When a single long piece of elastic wire is injected trough channels into a
confining two-dimensional cavity, a complex structure of hierarchical loops is
formed. In the limit of maximum packing density, these structures are described
by several scaling laws. In this paper it is investigated this packing process
but using plastic wires which give origin to completely irreversible structures
of different morphology. In particular, it is studied experimentally the
plastic deformation from circular to oblate configurations of crumpled wires,
obtained by the application of an axial strain. Among other things, it is shown
that in spite of plasticity, irreversibility, and very large deformations,
scaling is still observed.Comment: 5 pages, 6 figure
The Conserved Charges and Integrability of the Conformal Affine Toda Models
We construct infinite sets of local conserved charges for the conformal
affine Toda model. The technique involves the abelianization of the
two-dimensional gauge potentials satisfying the zero-curvature form of the
equations of motion. We find two infinite sets of chiral charges and apart from
two lowest spin charges all the remaining ones do not possess chiral densities.
Charges of different chiralities Poisson commute among themselves. We discuss
the algebraic properties of these charges and use the fundamental Poisson
bracket relation to show that the charges conserved in time are in involution.
Connections to other Toda models are established by taking particular limits.Comment: 18 pages, LaTeX, (one appendix and one reference added, small changes
in introduction and conclusions, eqs.(5.14) and (5.19) improved, final
version to appear in Int. J. Modern Phys. A
Constrained KP Models as Integrable Matrix Hierarchies
We formulate the constrained KP hierarchy (denoted by \cKP) as an
affine matrix integrable hierarchy generalizing the
Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded
structure of the generalized Drinfeld-Sokolov hierarchy, we are able to find
several new universal results valid for the \cKP hierarchy. In particular, our
method yields a closed expression for the second bracket obtained through Dirac
reduction of any untwisted affine Kac-Moody current algebra. An explicit
example is given for the case , for which a closed
expression for the general recursion operator is also obtained. We show how
isospectral flows are characterized and grouped according to the semisimple
{\em non-regular} element of and the content of the center of
the kernel of .Comment: LaTeX, 19 pg
Grassmanian and Bosonic Thirring Models with Jump Defects
In this paper we discuss the Lax formulation of the Grassmanian and Bosonic
Thirring models in the presence of jump defects. For the Grassmanian case, the
defect is described by B\"acklund transformation which is responsible for
preserving the integrability of the model.
We then propose an extension of the B\"acklund transformation for the Bosonic
Thirring model which is verified by some B\"acklund transitions like
Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and
Two solitons - Two solitons. The Lax formulation within the space split by the
defect leads to the integrability of Bosonic Thirring model.Comment: Latex 21 page
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