Related papers: Group classification of linear evolution equations
All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…
We consider infinite-dimensional parabolic rough evolution equations. Using regularizing properties of analytic semigroups we prove global-in-time existence of solutions and investigate random dynamical systems for such equations.
The present paper solves completely the problem of the group classification of nonlinear heat-conductivity equations of the form\ $u_{t}=F(t,x,u,u_{x})u_{xx} + G(t,x,u,u_{x})$. We have proved, in particular, that the above class contains no…
We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
We study Hodge representations of absolutely simple Q-algebraic groups with Hodge numbers h = (1,1,...,1). For those groups that are not of type A, we give a classification of the R-irreducible representations; a similar classification for…
We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending…
We give a Lie-algebraic classification of third order quasilinear equations which admit non-trivial Lie point symmetries.
We study integrable Euler equations on the Lie algebra $\mathfrak{gl}(3,\mathbb{R})$ by interpreting them as evolutions on the space of hexagons inscribed in a real cubic curve.
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…
Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…
The problem of classifying all unitary R-matrices of arbitrary finite dimension that have precisely two distinct eigenvalues is described, working up to a natural equivalence relation given by the characters of their braid group…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…
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…
Systems of nonlinear ordinary differential equations are constructed, for which the general solution is algebraically expressed in terms of a finite number of particular solutions. Expressions of that type are called the nonlinear…