Related papers: Nonautonomous mixed mKdV-sinh-Gordon hierarchy
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…
A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua…
The main purpose of this paper is to extend results, which have been obtained previously to describe the classical scattering of solitons with integrable defects of type I, to include the much larger and intricate collection of finite-gap…
The Hirota transformation for the soliton solutions of the classical Sine-Gordon equation is suggestive of an extremely simple way for the construction of a nonlinear quantum-dynamical system of spin 1/2 particles that is equivalent to the…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
In the framework of the Sine-Gordon (SG) theory we will present the construction of a dynamical Virasoro symmetry which has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although, it is non-local in the SG field theory,…
The Euclidean analogues of the sine-Gordon solitons are used as sources of the heterotic fivebrane solutions in the ten-dimensional heterotic string theory. Some properties of these soliton solutions are discussed. These solitons in…
In this work we start from the Higgs prototype model to introduce a new model, which makes a smooth transition between systems with well located minima and systems that support no minima at all. We implement this possibility using the…
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in terms of an adapted extension of standard vertex operators. A…
We extend the action for evolution equations of KdV and MKdV type which was derived in [Capel/Nijhoff] to the case of not periodic, but only equivariant phase space variables, introduced in [Faddeev/Volkov]. The difference of these…
Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform…
The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well…
A systematic group-theoretical analysis of the supersymmetric sinh-Gordon equation is performed. A generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction…
In this paper we study the sine-Gordon and the Liouville hierarchies in laboratory coordinates from a bi-Hamiltonian point of view. Besides the well-known local structure these hierarchies possess a second compatible non-local Poisson…
We investigate the classical and nonclassical reductions of the $2+1$-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalisation of the sine-Gordon equation. A family of solutions obtained as a nonclassical…
Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…
Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are…
One of the few schemes for obtaining an integrable nonultralocal quantum model is its possible generation from an ultralocal model by a suitable gauge transformation. Applying this scheme we discover two new nonultralocal models, which fit…
The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for…
We construct explicit multivortex solutions for the complex sine-Gordon equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the previously found (coaxial) multivortices, the new solutions comprise $n$ single vortices placed…