相关论文: Classification of discrete equations linearizable …

In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…

We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…

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.…

It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…

We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…

We give a Lie-algebraic classification of third order quasilinear equations which admit non-trivial Lie point symmetries.

Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…

A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…

We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the…

Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201…

We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax…

We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in the…

We give evaluations in closed form of certain non linear differential equations

In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to…

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…

We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…

We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its…

In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…