Finding non-polynomial positive invariants and lyapunov functions for polynomial systems through Darboux polynomials [PDF]
2014 American Control Conference, 2014 In this paper, we focus on finding positive invari-ants and Lyapunov functions to establish reachability and stability properties, respectively, of polynomial ordinary differential equations (ODEs). In general, the search for such functions is a hard problem.
Goubault, Eric +3 more
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Elementary Darboux transformations and factorization
, 2005 A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones.
A. B. Shabat +8 more
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On the Darboux-Nijenhuis Variables for the Open Toda Lattice [PDF]
, 2006 We discuss two known constructions proposed by Moser and by Sklyanin of the Darboux-Nijenhuis coordinates for the open Toda lattice.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics ...
Grigoryev, Yuriy A., Tsiganov, Andrey V.
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Uniform treatment of Darboux’s method and the Heisenberg polynomials [PDF]
Proceedings of the American Mathematical Society, 2013 We show that the set of Heisenberg polynomials furnishes a simple non-trivial example in the uniform treatment of Darboux's method.
Liu, Sai-Yu, Wong, R., Zhao, Yu-Qiu
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Deformed solitons of a typical set of (2+1)–dimensional complex modified Korteweg–de Vries equations
International Journal of Applied Mathematics and Computer Science, 2020 Deformed soliton solutions are studied in a typical set of (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) equations. Through constructing the determinant form of the n-fold Darboux transformation for these (2+1)-dimensional cmKdV equations,
Yuan Feng, Zhu Xiaoming, Wang Yulei
doaj +1 more source
From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition
, 2000 The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is
Arnold V I +17 more
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Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
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Finding Liouvillian first integrals of rational ODEs of any order in finite terms [PDF]
, 2005 It is known, due to Mordukhai-Boltovski, Ritt, Prelle, Singer, Christopher and others, that if a given rational ODE has a Liouvillian first integral then the corresponding integrating factor of the ODE must be of a very special form of a product of ...
Kosovtsov, Yuri N.
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Spectral curve, Darboux coordinates and Hamiltonian structure of periodic dressing chains
, 2002 A chain of one-dimensional Schr\"odinger operators connected by successive Darboux transformations is called the ``Darboux chain'' or ``dressing chain''. The periodic dressing chain with period $N$ has a control parameter $\alpha$.
Adams +21 more
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Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts [PDF]
, 2017 In our previous papers, the Wronskian identities for the Hermite, Laguerre and Jacobi polynomials and the Casoratian identities for the Askey-Wilson polynomial and its reduced form polynomials were presented.
Odake, Satoru
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