Results 151 to 160 of about 6,848 (171)

Darboux transformation and nonclassical orthogonal polynomials

Russian Physics Journal, 1995
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Samsonov, B. F., Ovcharov, I. N.
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Singular Points of Polynomial Darboux Systems

Qualitative Theory of Dynamical Systems, 2019
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Algebraic Traveling Wave Solutions, Darboux Polynomials and Polynomial Solutions

Qualitative Theory of Dynamical Systems, 2017
A 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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Burchnall–Chaundy polynomials and Dunkl–Darboux operators

Mathematical Notes, 2017
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First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

Physics Letters A, 2010
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García, Isaac A., Grau, Maite, Llibre, Jaume   +2 more
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Isospectral orthogonal polynomials from the Darboux transforms

International Journal of Quantum Chemistry, 2004
AbstractOrthogonal 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, J. Morales, E. Zamora‐Gallardo, J. García‐Ravelo   +3 more
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Existence and Degree of Darboux Polynomials

2017
This 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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Invariant hyperplanes and Darboux integrability of polynomial vector fields

Journal of Physics A: Mathematical and General, 2002
Summary: 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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A Christoffel-Darboux-Type Formula for Szegö Polynomials and Polynomial Evaluation

1999
Polynomials Φ n , n ≥ 0, orthogonal on the complex unit circle satisfy a recurrence relation. If we shift their recurrence coefficients, we obtain the associated polynomials, which can be modified by changing the initialization. We prove a dual recurrence relation and a mixed Christoffel-Darboux-type formula, which expresses the derivative of an ...
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2-Orthogonal polynomials and Darboux transformations. Applications to the discrete Hahn-classical case

Journal of Difference Equations and Applications, 2021
Francisco Marcellan
exaly