相关论文: Explicit solutions to the semi-discrete modified K…

In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all…

We propose a new analyzing method, which is called the tautological flow method, to analyze the integrability of partial difference equations (P$\Delta$Es) based on that of partial differential equations (PDEs). By using this method, we…

An optimal-velocity (OV) model describes car motion on a single lane road. In particular, near to the boundary signifying the onset of traffic jams, this model reduces to a perturbed Korteweg-de Vries (KdV) equation using asymptotic…

Twenty five years ago U. Pinkall discovered that the Korteweg-de Vries equation can be realized as an evolution of curves in centoraffine geometry. Since then, a number of authors interpreted various properties of KdV and its…

We consider a quasilinear KdV equation that admits compactly supported traveling wave solutions (compactons). This model is one of the most straightforward instances of degenerate dispersion, a phenomenon that appears in a variety of…

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…

This manuscript embarks on an in-depth exploration of the modified Korteweg-de Vries (mKdV) equation, with a particular emphasis on unraveling the intricate structure of its infinite symmetries and their physical interpretations. Central to…

We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of…

We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation $\partial_t u = -\partial_x (\partial_x^2 u + 3u^2-bu)$, where $b(x,t) = b_0(hx,ht)$, $h\ll 1$ is a slowly varying, but not small, potential. We option an…

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.

We study the integrability of mappings obtained as reductions of the discrete Korteweg-de Vries (KdV) equation and of two copies of the discrete potential Korteweg-de Vries equation (pKdV). We show that the mappings corresponding to the…

The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary…

Discrete models of the Dirac-K\"{a}hler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.

In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versions (using Darboux transformations) of the spectral problems…

We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate…

We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as $N$ tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like…

We continue the study of the Korteweg-de Vries equation in terms of cento-affine curves, initiated by U. Pinkall. A centro-affine curve is a closed parametric curve in the affine plane such that the determinant made by the position and the…

In this paper we investigate a time dependent family of plane closed Jordan curves evolving in the normal direction with a velocity which is assumed to be a function of the curvature, tangential angle and position vector of a curve. We…

Employing the Lax pairs of the noncommutative discrete potential Korteweg--de Vries (KdV) and Hirota's KdV equations, we derive differential--difference equations that are consistent with these systems and serve as their generalised…

The Baecklund transformation for the ultradiscrete KP equation is proposed. An algorithm to eliminate variables from the ultradiscrete linear equations is proposed. The consistency condition for the Baecklund transformation equations is…