Related papers: The Kundu--Eckhaus equation and its discretization…
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for…
A study is presented on the convergence of the computation of coupled advection-diffusion-reaction equations. In the computation, the equations with different coefficients and even types are assigned in two subdomains, and Schwarz iteration…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…
When a gas of particles interacts with much a larger reservoir the density dynamics on large scales is typically governed by diffusion. We study this paradigmatic problem for weakly coupled integrable systems and show that this picture gets…
We introduce the Burgers transform $\mathcal{B}$, a nonlinear bijection between holomorphic functions $f\colon U\to\mathbb{C}^+$ and rigid variable elliptic structures on the plane, defined implicitly by $\lambda = f(y-\lambda x)$. The…
We consider a class of variable coefficient Burgers equations in 2+1 dimensions and make use of their equivalence group to give a complete symmetry classification up to equivalence. Equivalence group is also applied to pick out the most…
R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general discretization scheme introduced by W. Kahan…
In this paper, we present an iterative reproducing kernel method for numerical solution of one dimensional fractional Burgers equation with variable coefficient. Convergence analysis is constructed theoretically. Numerical experiments show…
We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are…
We introduce the graded bialgebra deformations, which explain Andruskiewitsch-Schneider's liftings method. We also relate this graded bialgebra deformation with the corresponding graded bialgebra cohomology groups, which is the graded…
In this article, we investigate the (2+1)-dimensional damping forcing coupled Burgers equation, which is obtain by adding damping and forcing terms from couple Burgers equation. The Lax pair of the (2+1)-dimensional damping forcing coupled…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
We construct a Backlund transformation for the Geng-Xue system with the help of reciprocal and gauge transformations. Furthermore, we derive N-Backlund transformation for the Geng-Xue system resorting to Bianchi's permutability. As an…
The original Miura transformation, considered as a nonlinear potential transformation, is applicable to a continual class of evolution equations, not only to discrete integrable equations and their hierarchies. The same continual class of…
The three-dimensional Kepler problem is related to the four-dimensional isotropic harmonic oscillators by the Kustaanheimo-Stiefel Transformations. In the first part of this paper, we study how certain integrable mechanical billiards are…
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
The centralizer algebra of the action of the unitary group on the real tensor powers of its natural module, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with…
Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the Crocco transformation, with a first-order partial derivative taken as a new independent variable and a second-order…
We introduce a hybrid Cole-Hopf-Darboux transformation to relate solutions of nonlinear and linear second order differential equations and derive a sufficient condition for this correspondence. In particular we show that solutions of some…
In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation.…