Related papers: Geometric Approaches for Generating Prolongations …
This is the second in a series of papers on natural modification of the normal tractor connection in a parabolic geometry, which naturally prolongs an underlying overdetermined system of invariant differential equations. We give a short…
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do…
In this paper we present a system of two nonlinear partial differential equations of the second order, depending on the time and one spatial coordinate. It can be written as a system of two Burgers equations, which allows one to immediately…
The classical theory of prolongation of G-structures was generalized by N. Tanaka to a wide class of geometric structures (Tanaka structures), which are defined on a non-holonomic distribution. Examples of Tanaka structures include…
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 compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k<l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of…
A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic…
The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
The extension structure of the 2-dimensional current algebra of non-linear sigma models is analysed by introducing Kostant Sternberg $(L,M)$ systems. It is found that the algebra obeys a two step extension by abelian ideals. The second step…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
We show that the Drinfeld-Sokolov system of equations has a nontrivial prolongation structure. The closure process for prolongation algebra gives rise to the sl(4,c) algebra which is used to derive the scattering problem for the system of…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
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…
The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed…
We provide, through the framework of extended geometry, a geometrisation of the duality symmetries appearing in magical supergravities. A new ingredient is the general formulation of extended geometry with structure group of non-split real…
The Wahlquist-Estabrook prolongation method constructs for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We present some general properties of Wahlquist-Estabrook algebras for…
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…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent -2 are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.