Results 151 to 160 of about 8,235 (175)

Darboux Polynomials for Lie Algebras

IFAC Proceedings Volumes, 2011
Abstract Darboux polynomials and relative characteristic polynomials extend to time-invariant nonlinear systems the concept of eigenvector-eigenvalue pair for linear systems, and are, therefore, very useful to depict the behavior of the system. In this article, using tools such as Lie algebras, it is shown how Darboux polynomials can be characterized ...
MENINI, LAURA, TORNAMBE', ANTONIO
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The Darboux Polynomials and Integrability of Polynomial Levinson–Smith Differential Equations

International Journal of Bifurcation and Chaos, 2023
We provide the necessary and sufficient conditions of Liouvillian integrability for nondegenerate near infinity polynomial Levinson–Smith differential equations. These equations generalize Liénard equations and are used to describe self-sustained oscillations. Our results are valid for arbitrary degrees of the polynomials arising in the equations.
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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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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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DARBOUX POLYNOMIALS AND ALGEBRAIC INTEGRABILITY OF THE CHEN SYSTEM

International Journal of Bifurcation and Chaos, 2007
In this paper, we characterize all the Darboux polynomials of the Chen system, [Formula: see text], and prove that the system is not algebraic integrability. For proving the results, we use the weight homogeneous polynomials and the method of characteristics.
Lü, Tinghua, Zhang, Xiang
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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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