Related papers: Linearizability Criteria for Systems of Two Second…
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation…
In the first part of planned series of papers the formal general solutions to selection of 80 examples of different types of second order nonlinear PDEs in two independent variables with constant parameters are given. The main goal here is…
In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as…
The singularity structure of a second-order ordinary differential equation with polynomial coefficients often yields the type of solution. It is shown that the $\theta$-operator method can be used as a symbolic computational approach to…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
The aim of this article is to provide a method to prove the irreducibility of non-linear ordinary differential equations by means of the differential Galois group of their variational equations along algebraic solutions. We show that if the…
Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order…
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
We demonstrate the fact that linearity is a meaningful symmetry in the sense of Lie and Noether. The role played by that `linearity symmetry' in the quadrature of linear ordinary second-order differential equations is reviewed, by the use…
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz…
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions at resonance, in which the nonlinear boundary conditions perturbation is not necessarily required to…
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…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
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…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
We obtain closed-form solutions of several inhomogeneous Lienard equations by the factorization method. The two factorization conditions involved in the method are turned into a system of first-order differential equations containing the…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…
Modeling of a wide class of physical phenomena, such as crystal growth and flame propagation, leads to tracking fronts moving with curvature-dependent speed. When the speed is the curvature this leads to one of the classical degenerate…
Linearizability is the gold standard among algorithm designers for deducing the correctness of a distributed algorithm using implemented shared objects from the correctness of the corresponding algorithm using atomic versions of the same…
The theory of superposition rules for solutions of a Lie system of first-order differential equations is extended to deal with analogous systems of second-order and the theory is illustrated with the very rich example of Ermakov-like…