Related papers: Bidifferential calculus, matrix SIT and sine-Gordo…
Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon…
We reveal the origin and structure of self-consistent source extensions of integrable equations from the perspective of binary Darboux transformations. They arise via a deformation of the potential that is central in this method. As…
We propose a method by which to examine all possible partial difference Lax pairs that consist of 'two by two' discrete linear problems, where the matrices contain one separable term in each entry. We thereby derive new, higher-order…
The infinite-dimensional family of exact solutions of the Klein--Gordon equation is constructed by the hypercomplex method.
The Semi-Implicit Root solver (SIR) is an iterative method for globally convergent solution of systems of nonlinear equations. Since publication, SIR has proven robustness for a great variety of problems. We here present MATLAB and MAPLE…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
The classical sine-Gordon model is a two-dimensional integrable field theory, with particle like solutions the so-called solitons. Using its integrability one can define its quantum version without the process of canonical quantization.…
We analyze a generalization of the sine-Gordon equation in laboratory coordinates on the half-line. Using the Fokas transform method for the analysis of initial-boundary value problems for integrable PDEs, we show that the solution $u(x,t)$…
In this note, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of…
We implement the numerical inverse scattering transform (NIST) for the sine-Gordon equation in laboratory coordinates on the real line using the method developed by Trogdon, Olver and Deconinck. The NIST allows one to compute the solution…
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…
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…
Using the sine-Gordon model as the prime example an alternative approach to integrable boundary conditions for a theory restricted to a half-line is proposed. The main idea is to explore the consequences of taking into account 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…
We prove that the tau-function of the integrable discrete sine-Gordon model apart from the "standard" bilinar identities obeys a number of "non-standard" ones. They can be combined into a bivector 3-dimensional difference equation which is…
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
Higher order tensor inversion is possible for even order. We have shown that a tensor group endowed with the Einstein (contracted) product is isomorphic to the general linear group of degree $n$. With the isomorphic group structures, we…
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
We study a discrete Darboux transformation and construct the multi-soliton solutions in terms of ratio of determinants for integrable discrete sine-Gordon equation. We also calculate explicit expressions of single, double, triple, quad…