Related papers: On Generalized Wronskians
For a linear ODE with indeterminate coefficients, we explicitly exhibit a fundamental system of solutions, in terms of the coefficients. We show that the generalized Wronskians of the fundamental system are given by an action of the Schur…
The Wronskian determinants (for coefficients of higher-order differential operators on the affine real line or circle) satisfy the table of Jacobi-type quadratic identities for strong homotopy Lie algebras -- i.e. for a particular case of…
We show that classical Wilczynski--Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We explore geometric structures associated with equations…
We study the map which sends vectors of polynomials into their Wronski determinants. This defines a projection map of a Grassmann variety which we call a Wronski map. Our main result is computation of degrees of the real Wronski maps.…
We aim to identify the generating, ordinary differential equation (ODE) from a set of trajectories of a partially observed system. Our approach does not need prescribed basis functions to learn the ODE model, but only a rich set of Neural…
The generalised Wronskian of differential order $k\geqslant 1$ for $N$ functions $f_1$, $\ldots$, $f_N$ in $d\geqslant 1$ independent variables $x^1$, $\ldots$, $x^d$ is the determinant of the matrix with these functions' derivatives…
In this paper, we introduce a sub-family of the usual generalized Wronskians, that we call geometric generalized Wronskians. It is well-known that one can test linear dependance of holomorphic functions (of several variables) via the…
We derive an expression for the spectral determinant of a second-order elliptic differential operator $\mathcal{T}$ defined on the whole real line, in terms of the Wronskians of two particular solutions of the equation $\mathcal{T} u=0$.…
We study the theory of ordinary differential equations over a commutative finite dimensional real associative unital algebra $\mathcal{A}$. We call such problems $\mathcal{A}$-ODEs. If a function is real differentiable and its differential…
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or…
The Casoratian determinants are very important in the study of linear difference equation, just as the Wronskian determinants are very important in the study of linear ordinary differential equations. The Casoratian and Wronskian…
Wronski determinant (Wronskian) provides a compact form for $\tau$-functions that play roles in a large range of mathematical physics. In 1979 Matveev and Satsuma, independently, obtained solutions in Wronskian form for the…
A broad set of sufficient conditions consisting of systems of linear partial differential equations is presented which guarantees that the Wronskian determinant solves the Korteweg-de Vries equation in the bilinear form. A systematical…
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…
A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate…
Based on the Wronski determinant, we propose the construction of linearly independent and orthogonal functions in any Hilbert function space. The method requires only an initial function from the space of functions under consideration, that…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
Identification of fractional order systems is considered from an algebraic point of view. It allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no…
We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that…
In this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative. Later, we use these tools to…