Related papers: Complex sine-Gordon-2: a new algorithm for multivo…
We introduce a new spin-fermion mapping, for arbitrary spin $S$ generating the SU(2) group algebra, that constitutes a natural generalization of the Jordan-Wigner transformation for $S=1/2$. The mapping, valid for regular lattices in any…
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key…
We study locally harmonic maps between a Riemann surface or Lorentz surface $M$ and a Riemann surface or Lorentz surface $N$. {All four cases are studied in a unified way}. All four cases are written using a unified formalism. Therefore…
Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling…
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…
Traditionally, Double Sine-Gordon Equation (DSGE) is seen as a nonintegrable equation. That means we cannot find general solutions in asymmetry DSGE. In this paper, we develop analytical method to solve this equation by Mobius…
The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified…
Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using the variables introduced in previous part of the work.
In this paper we derive the equations of motion for two-layer point vortex motion on the upper half plane. We study the invariants using symmetry, including the Hamiltonian and show that the two vortex problem is integrable. We characterize…
In this paper we consider the integrability of the mappings derived from the double discrete related sine-Gordon $(\Delta \Delta RsG)$ equation, which we recently introduced in the paper Higher dimensional integrable mappings, under an…
Two sets of super Riccati equations are presented which result in two linear problems of super sine-Gordon equation. The linear problems are then shown to be related to each other by a super gauge transformation and to the super…
The sine-Gordon expansion method; which is a transformation of the sine-Gordon equation has been applied to the potential-YTSF equation of dimension (3+1) and the reaction-diffusion equation. We obtain new solitons of this equation in the…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
Analytical and numerical vortex solutions for the extended Skyrme-Faddeev model in a (3+1) dimensional Minkowski space-time are investigated. The extension is obtained by adding to the Lagrangian a quartic term, which is the square of the…
A general and systematic regularization is developed for the exact solitonic form factors of exponential operators in the (1+1)-dimensional sine-Gordon model by analytical continuation of their integral representations. The procedure is…
We demonstrate the way to derive the second Painlev\'e equation $P_2$ and its B\"acklund transformations from the deformations of the Nonlinear Schr\"odinger equation (NLS), all the while preserving the strict invariance with respect to the…
We propose a nonlinear $\sigma$-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean…
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…
In this article, we study the numerical solution of the one dimensional nonlinear sine-Gordon by using the modified cubic B-spline differential quadrature method. The scheme is a combination of a modified cubic B spline basis function and…
A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner…