相关论文: Integrability of Riccati equation from a group the…

The article presents a rather surprising Floquet-type representation of time-varying transition matrices associated with a class of nonlinear matrix differential Riccati equations. The main difference with conventional Floquet theory comes…

We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…

A general theoretical framework based on group-subgroup and group-supergroup relations is proposed to describe and to derive interpenetrating nets.

A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…

Three comparison criteria are obtained for second order Riccati equations. On the basis of these criteria some global existence theorems are proved mentioned equations. The results obtained are used to derive a non oscillation criterion for…

Respecting deformational constraints and predeformations poses a substantial challenge in the description of nonlinear elasticity. We here outline how group theory can play a beneficial role to overcome this challenge. Specifically, group…

Using the S.Lie's infinitesimal approach we establish the connection between integrability of a one-parameter family of the Riccati equations and the stationary KdV hierarchy.

We study 2D non-linear sigma models on a group manifold with a special form of the metric. We address the question of integrability for this special class of sigma models. We derive two algebraic conditions for the metric on the group…

Using N. Euler's theorem on the integrability of the general anharmonic oscillator equation \cite{12}, we present three distinct classes of general solutions of the highly nonlinear second order ordinary differential equation…

In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.

A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…

The control algebraic Riccati equation is studied for a class of systems with unbounded control and observation operators. Using a dichotomy property of the associated Hamiltonian operator matrix, two invariant graph subspaces are…

In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here that the error of the approximate solution to the operator-valued Riccati equation is…

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of…

Differential Galois theory has played important roles in the theory of integrability of linear differential equation. In this paper we will extend the theory to nonlinear case and study the integrability of the first order nonlinear…

The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory…

Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…

As it is popular known, Riccati equation is the key basic tool for optimal control in the modern control theory. The solvability conditions of optimal control, stabilization conditions and controller design are all based on the Riccati…

Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.