Related papers: On contact symmetries of evolution equations
We give examples of contactomorphisms in every dimension that are smoothly isotopic to the identity but that are not contact isotopic to the identity. In fact, we prove the stronger statement that they are not even symplectically…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
In this paper, we unearth symmetries of different types of a nonlinear non-polynomial oscillator. The symmetries which we report here are adjoint-symmetries, contact symmetries and telescopic vector fields. We also obtain Jacobi last…
The survey is devoted to algebraic structures related to integrable ODEs and evolution PDEs. A description of Lax representations is given in terms of vector space decomposition of loop algebras into a direct sum of Taylor series and a…
One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric…
The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras…
This paper develops the technique of constructing Lax representations for PDEs via non-central extensions generated by non-triivial exotic 2-cocycles of their contact symmetry algebras. We show that the method is applicable to the Lax…
On an equation associated with the contact Lie algebras/ Mikhail V. Saveliev/ In the framework of a Lie algebraic approach we study a nonlinear equation associated with the contact Lie algebra ${\bf K}K_m$, that seems to be relavant for…
In the present paper the non-Noether symmetries of the Toda model, nonlinear Schodinger equation and Korteweg-de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in…
This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial…
Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In this paper, we present a class of scalar second-order PDEs…
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…
For a large class of nonlinear evolution PDEs, and more generally, of nonlinear semigroups, as well as their approximating numerical methods, two rather natural stability type convergence conditions are given, one being necessary, while the…
In this paper, we extend the well-known Noether theorem for Lagrangian systems to contact Lagrangian systems. We introduce a classification of infinitesimal symmetries and obtain the corresponding dissipated quantities. We notice that in…
This article studies the set of R-equivalence classes of the group of proper projective similitudes of an algebra with involution of the first kind. The main results concern base fields of characteristic different from 2 over which every…
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…
We study CR-manifolds of arbitrary CR codimension, mainly focusing on Levi and contact-nondegeneracy and depth. We investigate these and other invariants in the locally homogeneous case, developing a comprehensive theory which establishes…
The moving coframe method is applied to solve the local equivalence problem for the class of nonlinear wave equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.
Using the symmetry approach, we find a class of integrable nonlinear PDEs with dispersion law $\omega(k)=k^{\frac32}$. All these equations turn out to be linearizable by means of a differential parametrization.