Related papers: Integral equivalence of multidimensional different…
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems.…
Many systems of interest to control engineering can be modeled by linear complementarity problems. We introduce a new notion of equivalence between linear complementarity problems that sets the basis to translate the powerful tools of…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
Geometrical properties of holonomic and non holonomic varieties defined by the Pfaff equations connected with a first order systems of differential equations are studied. The Riemann extensions of affine connected spaces for investigation…
We study the validity of an extension of Frobenius theorem on integral manifolds for some classes of Pfaff-type systems of partial differential equations involving multidimensional "rough" signals, i.e. "differentials" of given H\"older…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We introduce perfect resolving algebras and study their fundamental properties. These algebras are basic for our theory of differential graded schemes, as they give rise to affine differential graded schemes. We also introduce etale…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
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…
Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
This paper is devoted to a study of linear, differential and topological classifications for linear controlled systems governed by ordinary differential equations. The necessary and sufficient conditions for the linear and topological…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant…
A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…