相关论文: Classification of scalar second-order differential…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
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…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
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 describe a way of solving a partial differential equation using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products…
We consider differential-algebraic equations in infinite dimensional state spaces and study, under which conditions we can associate a $C_{0}$-semigroup with such equations. We determine the right space of initial values and characterise…
We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the…
In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and…
An exhaustive group classification of variable coefficient generalized Kawahara equations is carried out. As a result, we derive new variable coefficient nonlinear models admitting Lie symmetry extensions. All inequivalent Lie reductions of…
A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…
We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We develop some calculation schemes to determine dynamics of a wide class of integrable quantum-optical models using their symmetry adapted reformulation in terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on "diagonal"…
Three-dimensional bicovariant differential calculus on the quantum group SU_q(2) is constructed using the approach based on global covariance under the action of the stabilizing subgroup U(1). Explicit representations of possible q-deformed…