Homogeneous darboux polynomials and generalising integrable ODE systems
Journal of Computational Dynamics, 2021 We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.
van der Kamp, Peter H. +2 more
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Darboux and rational first integrals for a family of cubic three dimensional system
Zanco Journal of Pure and Applied Sciences, 2021 In this paper, we investigate the first integrals of the following system where and , . This kind of system is a special case of three-dimensional polynomial cubic differential systems.
Sarbast H. Mikaeel , Azad I. Amen
doaj
Asymptotics of Meixner polynomials and Christoffel–Darboux kernels [PDF]
Transactions of the Moscow Mathematical Society, 2013 Summary: We obtain the asymptotics of the classical Meixner polynomials \(M_n(x)\) (orthogonal with respect to a discrete measure supported at the nonnegative integer points) and the corresponding reproducing kernels (Christoffel-Darboux kernels) \(K_n(x,y)\) as \(n\) and the variable \(x\) tend to infinity under various relationships between their ...
Aptekarev, A. I., Tulyakov, D. N.
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The role of algebraic solutions in planar polynomial differential systems [PDF]
, 2005 We study a planar polynomial differential system, given by \dot{x}=P(x,y), \dot{y}=Q(x,y). We consider a function I(x,y)=\exp \{h_2(x) A_1(x,y) \diagup A_0(x,y) \} h_1(x) \prod_{i=1}^{\ell} (y-g_i(x))^{\alpha_i}, where g_i(x) are algebraic functions, A_1(
Giacomini, Héctor +2 more
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Divergence-free polynomial derivations [PDF]
, 2017 In this paper we present some new and old properties of divergences and divergence-free ...
Nowicki, Andrzej
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Disturbance Dynamics and Its Effects on Carbon in Human-Impacted Mountain Forests in Northwestern Yunnan, China. [PDF]
Ecol EvolIdentifying and quantifying natural and anthropogenic disturbances at fine spatial scales is critical to assess the role of forests in climate change mitigation. Using tree rings, fire scars, satellite imagery, official records, and interviews, we reconstructed historical disturbances and identified fires, logging events, landslides, and icy ...
Cheng Z, Aakala T, Ji C, Larjavaara M.
europepmc +2 more sources
Realization problems for limit cycles of planar polynomial vector fields [PDF]
, 2015 We show that for any finite configuration of closed curves $\Gamma\subset \mathbb{R}^2$, one can construct an explicit planar polynomial vector field that realizes $\Gamma$, up to homeomorphism, as the set of its limit cycles with prescribed periods ...
Margalef-Bentabol, Juan +1 more
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Binary Bell polynomials and Darboux covariant Lax pairs [PDF]
Glasgow Mathematical Journal, 2001 Hirota representations of soliton equations have proved very useful. They produced many of the known families of multisoliton solutions, and have often led to a disclosure of the underlying Lax systems and infinite sets of conserved quantities. A striking feature is the ease with which direct insight can be gained into the nature of the eigenvalue ...
Lambert, Franklin +2 more
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Non-polynomial extensions of solvable potentials a la Abraham-Moses [PDF]
, 2013 Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics.
Darboux G., Ryu Sasaki, Satoru Odake
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A Christoffel–Darboux formula for multiple orthogonal polynomials
Journal of Approximation Theory, 2004 11 pages, no ...
Daems, E., Kuijlaars, A.B.J.
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