相关论文: On the point transformations for the second order …
Within the framework of inverse Lie problem, we give some non-trivial examples of coupled Lie remarkable equations, \textit{i.e.}, classes of differential equations that are in correspondence with their Lie point symmetries. In particular,…
Existence and uniqueness of solutions for $\alpha\in\left( 2,3\right] $ order fractional differential equations with three point fractional boundary and integral conditions is discussed. The results are obtained by using standard fixed…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
A class of partial differential equations (a conservation law and four balance laws), with four independent variables and involving sixteen arbitrary continuously differentiable functions, is considered in the framework of equivalence…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the…
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+\Omega y$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a…
We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
In this paper, we study differential operators associated with the formal expression $y''' + s(\sigma' y)' + s \sigma' y' + \kappa \sigma'' y$ with distribution coefficient $\sigma'' \in W_3^{-2}$, where $s$ and $\kappa$ are constants. The…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
We look for differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to the classical weight function for the Jacobi polynomials together with point masses at both…
The purpose of this paper is to generalize the self-duality equation by Tchrakian and Corrigan et. al.. Novel generalized self-duality equations on higher-dimensional spaces are discussed. This class of equations includes the usual…
The goal of the present paper is to propose an enhanced ordinary differential equations solver by exploitation of the powerful equivalence method of \'Elie Cartan. This solver returns a target equation equivalent to the equation to be…
In this paper, the Hankel transform of the generalized q-exponential polynomial of the first form (q, r)-Whitney numbers of the second kind is established using the method of Cigler. Consequently, the Hankel transform of the first form (q,…
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations were listed and discussed in detail. We indicate two more…