Results 21 to 30 of about 6,848 (171)

The combined KdV-mKdV equation: Bilinear approach and rational solutions with free multi-parameters

Results in Physics, 2023
In this paper, we investigate the combined KdV-mKdV equation which serves as a valuable tool in the study of water waves, enabling researchers to understand and predict the behaviour of various wave phenomena, including solitary waves, wave breaking ...
Rui-rui Yuan, Ying Shi, Song-lin Zhao, Jun-xiao Zhao   +3 more
doaj   +1 more source

Necessary and sufficient conditions for the existence of invariant algebraic curves

Electronic Journal of Qualitative Theory of Differential Equations, 2021
We present a set of conditions enabling a polynomial system of ordinary differential equations in the plane to have invariant algebraic curves. These conditions are necessary and sufficient. Our main tools include factorizations over the field of Puiseux
Maria Demina
doaj   +1 more source

Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms, 2021
Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0.
Juan Carlos García-Ardila, Francisco Marcellán   +1 more
doaj   +1 more source

On Determinant Expansions for Hankel Operators

Concrete Operators, 2020
Let w be a semiclassical weight that is generic in Magnus’s sense, and (pn)n=0∞({p_n})_{n = 0}^\infty the corresponding sequence of orthogonal polynomials. We express the Christoffel–Darboux kernel as a sum of products of Hankel integral operators.
Blower Gordon, Chen Yang
doaj   +1 more source

Derivations of polynomial algebras without Darboux polynomials

Journal of Pure and Applied Algebra, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ollagnier, Jean Moulin, Nowicki, Andrzej
openaire   +2 more sources

Darboux polynomials, balances and Painlevé property [PDF]

Regular and Chaotic Dynamics, 2017
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of the system and the Painlevé property. As far as we know, these are the first results which relate the Darboux theory of integrability, first, to the Painlevé property and, second, to the Kovalevskaya ...
Llibre, Jaume, Valls, Clàudia
openaire   +2 more sources

Confluent Chains of DBT: Enlarged Shape Invariance and New Orthogonal Polynomials [PDF]

, 2015
We construct rational extensions of the Darboux-P\"oschl-Teller and isotonic potentials via two-step confluent Darboux transformations. The former are strictly isospectral to the initial potential, whereas the latter are only quasi-isospectral.
Grandati, Yves, Quesne, Christiane
core   +3 more sources

On the Darboux Integrability of Polynomial Differential Systems [PDF]

Qualitative Theory of Dynamical Systems, 2011
A method to find explicit closed forms for a first integral of a planar polynomial differential system from its invariant algebraic curves was given by \textit{G. Darboux} [C. R. LXXXVI, 581--586 (1878; JFM 10.0214.03)]. From that moment on, many research articles were devoted to the study of the integrability problem by using the invariant algebraic ...
Llibre, Jaume, Zhang, Xiang
openaire   +2 more sources

Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV [PDF]

, 2006
This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials, which were first given ...
A. Mostafazadeh, A. N. Sissakian, A. Ushveridze, B. Bagchi, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. Grosche, C. M. Bender, Ch. Grosche, D. Peak, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, E. G. Kalnins, F. Cannata, G. Koenigs, G. S. Pogosyan, H. Kleinert, I. S. Gradshteyn, I. V. Lutsenko, J. Fris, L. S. Schulman, M. A. Olmo Del, M. Böhm, M. N. Olevskii, M. Znojil, M. Znojil, M. Znojil, N. W. Evans, P. Winternitz, R.P. Feynman, S. Wojciechowski   +49 more
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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.
core   +5 more sources