23,795 research outputs found

### Classical Integrable N=1 and $N= 2$ 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

### T-Duality in 2-D Integrable Models

The non-conformal analog of abelian T-duality transformations relating pairs
of axial and vector integrable models from the non abelian affine Toda family
is constructed and studied in detail.Comment: 14 pages, Latex, v.2 misprints corrected, reference added, to appear
in J. Phys.

### Dressing approach to the nonvanishing boundary value problem for the AKNS hierarchy

We propose an approach to the nonvanishing boundary value problem for
integrable hierarchies based on the dressing method. Then we apply the method
to the AKNS hierarchy. The solutions are found by introducing appropriate
vertex operators that takes into account the boundary conditions.Comment: Published version Proc. Quantum Theory and Symmetries 7
(QTS7)(Prague, Czech Republic, 2011

### Affine Lie Algebraic Origin of Constrained KP Hierarchies

We present an affine $sl (n+1)$ algebraic construction of the basic
constrained KP hierarchy. This hierarchy is analyzed using two approaches,
namely linear matrix eigenvalue problem on hermitian symmetric space and
constrained KP Lax formulation and we show that these approaches are
equivalent. The model is recognized to be the generalized non-linear
Schr\"{o}dinger (\GNLS) hierarchy and it is used as a building block for a
new class of constrained KP hierarchies. These constrained KP hierarchies are
connected via similarity-B\"{a}cklund transformations and interpolate between
\GNLS and multi-boson KP-Toda hierarchies. Our construction uncovers origin
of the Toda lattice structure behind the latter hierarchy.Comment: 25 pgs, LaTeX, IFT-P/029/94 and UICHEP-TH/93-1

### Darboux-Backlund Derivation of Rational Solutions of the Painleve IV Equation

Rational solutions of the Painleve IV equation are constructed in the setting
of pseudo-differential Lax formalism describing AKNS hierarchy subject to the
additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian
representations for rational solutions are obtained by successive actions of
the Darboux-Backlund transformations.Comment: 21 page

### On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation

Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled
by an angle $\theta$ are constructed and then reduced to the two-component
Camassa--Holm model. Only three different independent classes of reductions are
encountered corresponding to the angle $\theta$ being 0, $\pi/2$ or taking any
value in the interval $0<\theta<\pi/2$. This construction induces B\"{a}cklund
transformations between solutions of the two-component Camassa--Holm model
associated with different classes of reduction.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA

### Integrable Origins of Higher Order Painleve Equations

Higher order Painleve equations invariant under extended affine Weyl groups
$A^{(1)}_n$ are obtained through self-similarity limit of a class of
pseudo-differential Lax hierarchies with symmetry inherited from the underlying
generalized Volterra lattice structure.Comment: 18 pages Late

- …