Related papers: Linearizability for third order evolution equation…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…
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…
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 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…
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…
We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
We show that one can define through the symmetry approach a procedure to check the linearizability of a difference equation via a point or a discrete Cole-Hopf transformation. If the equation is linearizable the symmetry provides the…
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…
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 group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
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…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We give a classification of all third-order nonlinear evolution equations which admit solvable Lie symmetry algebras $\mathsf{A}$ and which are not linearized. We have found that there are 48 types of equations for $\dim\mathsf{A}=3$, 88…
We consider here the class of fully-nonlinear symmetry-integrable third-order evolution equations in 1+1 dimensions that were proposed recently in the journal Open Communications in Nonlinear Mathematical Physics, vol. 2, 216--228 (2022).…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from…