Related papers: Complex sine-Gordon-2: a new algorithm for multivo…
Recently we proposed a decomposition for fields of the Georgi-Glashow model and interpreted Cho's decomposition as a result of some constraints on Georgi-Glashow's fields. Now, using the decomposition form that Faddeev and Niemi proposed,…
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…
We modify the recently proposed model of Speight and Ward to make it possess time dependent solutions. We find that for each lattice spacing and for each velocity of the sine Gordon kink we can find a modification of the model for which…
The Lax representation and Backlund transformations for the systems similar to WZNW (Wess-Zumino-Novicov-Witten) systems and non-abelian affine Toda models are obtained in present paper. One of these systems is a new integrable extension of…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
The geometric model of the pathway linking Schlesinger and Garnier--Painlev\'e~6 systems based on an original orthonormalization of a set of elements in ${sl(2,\mathbb C)}$ is constructed. The explicit polynomial map of the Cartesian…
We find a system of two polynomial equations in two unknowns, whose solution allows to give an explicit expression of the conformal representation of a simply connected three sheeted compact Riemann surface onto the extended complex plane.…
Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram…
The study of superfluid quantum vortices has long been an important area of research, with previous work naturally focusing on two-dimensional and three-dimensional systems, where rotation stabilises point vortices and line vortices…
By using B\"acklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ are generated from a seed which corresponds to Lipschitz surfaces of…
We point out novel connections between complex PT-invariant solutions of several nonlinear equations such as $\phi^4$, $\phi^6$, sine-Gordon, hyperbolic sine-Gordon, double sine-Gordon, double hyperbolic sine-Gordon, mKdV, etc. We then use…
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces in two and three dimensions. The kernel…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
Self-gravitational force calculation for infinitesimally thin disks is important for studies on the evolution of galactic and protoplanetary disks. Although high-order methods have been developed for hydrodynamic and magneto-hydrodynamic…
We study the perturbed sine-Gordon equation $\theta_{tt}-\theta_{xx}+\sin \theta= F(\varepsilon,x)$, where we assume that the perturbation $F$ is analytic in $\varepsilon$ and that its derivatives with respect to $\varepsilon$ satisfy…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
We apply a recently developed method to exactly solve the $\Phi^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a…
We consider a hierarchy of classical Liouville completely integrable models sharing the same (linear) $r$--matrix structure obtained through an $N$--th jet--extension of $\mathfrak{su}(2)$ rational Gaudin models. The main goal of the…
A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic…
In this paper, we propose a reproducing kernel Hilbert space method (RKHSM) for solving the sine--Gordon (SG) equation with initial and boundary conditions based on the reproducing kernel theory. Its exact solution is represented in the…