相关论文: Complex sine-Gordon-2: a new algorithm for multivo…
It is shown, how to generate infinite sequences of differential equations of the second order based on some standard equations, using Euler-Imshenetsky-Darboux (EID) transformation. For all this, factorizations of differential operators and…
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 propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of…
We consider an integrable generalization of the sine-Gordon (sG) equation that was earlier derived by one of the authors using bi-Hamiltonian methods. This equation is related to the sG equation in the same way that the Camassa-Holm…
In this paper, we introduce two new modified inertial Mann Halpern and viscosity algorithms for solving fixed point problems. We establish strong convergence theorems under some suitable conditions. Finally, our algorithms are applied to…
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
In this paper we describe the integral transform that allows to write solutions of one partial differential equation via solution of another one. This transform was suggested by the author in the case when the last equation is a wave…
We develop numerical methods for solving the spin-2 Gross-Pitaevskii equation. The basis of our work is a two-way splitting of this evolution equation that leads to two exactly solvable subsystems. Utilizing second-order and fourth-order…
This work deals with a new family of models, which includes the sine-Gordon model and the double-sine-Gordon, triple-sine-Gordon and so on. The investigation is based on a deformation procedure, which is used to deform a well-known model,…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…
It is shown fields that cannot be represented over one complex plane can be further decomposed for representation over multiple complex planes. This finding is demonstrated here by solving of the Schr\"{o}dinger equation for the hydrogen…
This article explores solutions to a generalised form of the Seiberg--Witten equations in higher dimensions, first introduced by Fine and the author. Starting with an oriented $n$ dimensional Riemannian manifold with a…
Another connection of harmonic maps to gravity is presented. Using 1-soliton and anti-soliton solutions of the sine-Gordon equation, we construct a pair of harmonic maps that we express in terms of a particular dilaton field in…
In this paper, we consider the second-order cone tensor eigenvalue complementarity problem (SOCTEiCP) and present three different reformulations to the model under consideration. Specifically, for the general SOCTEiCP, we first show its…
We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…
We delve into the inverse scattering transform of the real-valued vector modified Korteweg--de Vries equation, emphasizing the challenges posed by $N$ pairs of higher-order poles in the transmission coefficient and the enhanced spectral…
This paper has two purposes. First we present a new definition of the multivariate Pad\'e approximation, a new fast numerical method. Then numerical solution of the one-dimensional (1D) time-dependent nonlinear Sine-Gordon equation (SGE) is…
A chain of transformations is found which relates one new integrable case of the generalized short pulse equation of Hone, Novikov and Wang [arXiv:1612.02481] with the sine-Gordon equation.