相关论文: On a nonlinear integrable difference equation on t…

The nonlinear selfdual variational principle established in a preceeding paper [8] -- though good enough to be readily applicable in many stationary nonlinear partial differential equations -- did not however cover the case of nonlinear…

Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other…

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax representations. There are also some other methods which are based on integrable scalar nonlinear partial…

Nonlinear tranlational symmetric equilibria with up to quartic flux terms in the free functions, reversed magnetic shear and sheared flow are constructed in two ways: i) quasianalytically by an ansatz which reduces the pertinent generalized…

A nonlinear modification of a parabolic Cauchy problem for entire functions of a single complex variable is considered. The modification means that the time half-line is divided onto the intervals of equal length and on each such interval…

The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…

We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…

The Adler sum rule states that the integral over energy of a difference of neutrino-nucleon and antineutrino-nucleon structure functions is a constant, independent of the four-momentum transfer squared. This constancy is a consequence of…

Consistently fitting vanilla option surfaces is an important issue when it comes to modelling in finance. Local volatility models introduced by Dupire in 1994 are widely used to price and manage the risks of structured products. However,…

We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are…

We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work…

A coupled system of non-linear partial differential equations is presented which describes non-perturbatively the evolution of deformations of a relativistic membrane of arbitrary dimension, $D$, in an arbitrary background spacetime. These…

In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouville type) for some nonlinear differential equations. The key…

We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…

For a one-dimensional wave equation, we consider a mixed problem in a curvilinear half-strip. The initial conditions have a first-kind discontinuity at one point. The mixed problem models the problem of a longitudinal impact on a finite…

Many physical problems can be described using the integral equations known as Volterra equations. There exists quite a number of analytical methods that can handle these equations for linear cases. For non-linear cases, a numerical scheme…

In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integro-differential Volterra convolution equations. We highlight in general how the pointwise behaviour of perturbation…

Integrable fractional equations such as the fractional Korteweg-deVries and nonlinear Schr\"odinger equations are key to the intersection of nonlinear dynamics and fractional calculus. In this manuscript, the first discrete/differential…