Related papers: Linearization through symmetries for discrete equa…
We provide a complete set of linearizability conditions for nonlinear partial difference equations de- fined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of…
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
In this paper we propose some linearizability tests of partial difference equations on a quad-graph given by one point, two points and generalized Hopf-Cole transformations. We apply the so obtained tests to a set of nontrivial examples.
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalized symmetries is constructed. We build modified series by…
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
A characterization of the symmetry algebra of the $n$th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines…
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…
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 linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorithmic.
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific…
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…