Related papers: First integrals of ordinary linear differential sy…
In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
The paper presents a new method for finding first integrals of ordinary difference equations which do not possess Lagrangians, nor Hamiltonians. As an example we solve a third order nonlinear ordinary differential equation and its invariant…
Let $L$ be the $n$-th order linear differential operator $Ly = \phi_0y^{(n)} + \phi_1y^{(n-1)} + \cdots + \phi_ny$ with variable coefficients. A representation is given for $n$ linearly independent solutions of $Ly=\lambda r y$ as power…
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…
Liouville integrable separable systems with quadratic in momenta first integrals are considered. Particular attention is paid to the systems generated by the so-called special conformal Killing tensors, i.e. Benenti systems. Then,…
We study the existence of real-analytic first integrals and real-analytic integrability for perturbations of integrable systems in the sense of Bogoyavlenskij including non-Hamiltonian ones. We especially assume that there exists a family…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particularly we are interested in the three-dimensional cubic…
The discrete gradient approach is generalized to yield integral preserving methods for differential equations in Lie groups.
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
The conditions of cylindricality and autonomy of first integrals, last multipliers and integral manifolds for linear homogeneous systems of partial differential equations and total differential systems are established.
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
A new approach for integration of the initial value problem for ordinary differential equations is suggested. The algorithm is based on approximation of the solution by a system of functions that contains orthogonal exponential polynomials.
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is…
This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…