Results 131 to 140 of about 187 (156)
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Singular Points of Polynomial Darboux Systems
Qualitative Theory of Dynamical Systems, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Darboux transformation and nonclassical orthogonal polynomials
Russian Physics Journal, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Samsonov, B. F., Ovcharov, I. N.
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A Mathematica Package for Certifying the Nonexistence of Darboux Polynomials
ACM Communications in Computer AlgebraWe present a Mathematica package to help investigate the existence of Darboux polynomials for (polynomial) ordinary differential equations (ODE). If we denote the derivation encoded by a given ODE by D , the package infers and propagates necessary conditions for a generic ansatz p
Maxime Bridoux, Khalil Ghorbal
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Constants and Darboux Polynomials for Tensor Products of Polynomial Algebras with Derivations
Communications in Algebra, 2004Let d 1 : k[X] → k[X] and d 2 : k[Y] → k[Y] be k-derivations, where k[X] ≔ k[x 1,…,x n ], k[Y] ≔ k[y 1,…,y m ] are polynomial algebras over a field k of characteristic zero.
Jean Moulin Ollagnier, Andrzej Nowicki
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Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions
Qualitative Theory of Dynamical Systems, 2017A traveling wave solution \(u= U(x-ct)\) of a partial differential equation \(u_{xx}= F(u,u_x,u_t)\) is called an algebraic traveling wave solution if there exists a polynomial \(p\) such that \(p(U,U')= 0\). The author completely characterizes the existence of algebraic traveling wave solutions of the partial differential equation \[ u_t= du_{xx}- a(u-
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First integrals and Darboux polynomials of natural polynomial Hamiltonian systems
Physics Letters A, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García, Isaac A. +2 more
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Burchnall–Chaundy polynomials and Dunkl–Darboux operators
Mathematical Notes, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Existence and Degree of Darboux Polynomials
2017This chapter presents results on the degree and existence of Darboux polynomials with an emphasis on invariant algebraic curves. We also introduce some tools and methods for characterizing the Darboux polynomials of polynomial vector fields.
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Isospectral orthogonal polynomials from the Darboux transforms
International Journal of Quantum Chemistry, 2004AbstractOrthogonal polynomials (OP) are used in many branches of the mathematical and physical sciences; in particular they are part of the eigenfunctions of quantum chemical (QC) potential models. Recently, in the search for new solvable potentials to be useful in QC applications, the use of supersymmetry (SUSY) and Hamiltonian intertwining methods ...
J. J. Peña +3 more
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Invariant hyperplanes and Darboux integrability of polynomial vector fields
Journal of Physics A: Mathematical and General, 2002Summary: This paper is composed of two parts. In the first part, we provide an upper bound for the number of invariant hyperplanes of the polynomial vector fields in \(n\) variables. This result generalizes those given by \textit{J. C. Artés, B. Grünbaum} and \textit{J. Llibre} [Pac. J. Math. 184, No.
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