Related papers: Inverse variational problem for equations in the R…
The transformation of the Nth- order linear difference equation into a system of the first order difference equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of the first…
We generalize the classical Lie results on a basis of differential invariants for a one-parameter group of local transformations to the case of arbitrary number of independent and dependent variables. It is proved that if universal…
A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytic general solution is presented,…
We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the…
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is…
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
A canonical system is a kind of first-order system of ordinary differential equations on an interval of the real line parametrized by complex numbers. It is known that any solution of a canonical system generates an entire function of the…
Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a…
Li\'enard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Li\'enard-type equations which admits a non-standard autonomous Lagrangian. As a by-product…
A generalised inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrodinger equation, proposed by…
A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation,…
A method to find exact solutions to nonlinear Schr\"odinger equation, defined on a line and on a plane, is found by connecting it with second order linear ordinary differential equation. The connection is essentially made using Riccati…
In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational…
An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
A new perspective on the classical mechanical formulation of particle trajectories in lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant Lagrangian…
A novel formulation of the Lie-Darboux method of obtaining the Riccati equations for the spatial curves in Euclidean three-dimensional space is presented. It leads to two Riccati equations that differ by the sign of torsion. The case of…