Results 21 to 30 of about 6,081 (189)
On the discretization of Darboux Integrable Systems [PDF]
Journal of Nonlinear Mathematical Physics, 2020 We study the discretization of Darboux integrable systems. The discretization is done using $x$-, $y$-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
Zheltukhin, K., Zheltukhina, Natalya
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Discrete Dynamics in Nature and Society, 2018 An integrable family of the different-difference equations is derived from a discrete matrix spectral problem by the discrete zero curvature representation. Hamiltonian structure of obtained integrable family is established.
Xi-Xiang Xu, Meng Xu
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Darboux integrability and the inverse integrating factor
Journal of Differential Equations, 2003 Consider planar (real or complex) polynomial vector fields \(X=P(x,y)\partial_x+Q(x,y)\partial_y\) having a Darboux first integral of the form \[ H= f_1^{\lambda_1}\cdots f_p^{\lambda_p} \left( \exp\left( {h_1}\over {g_1} \right) \right)^{\mu_1} \cdots \left( \exp\left({h_q}\over{g_q} \right) \right)^{\mu_q}, \] where \(f_i, g_i\) and \(h_i\) are ...
Chavarriga, Javier +3 more
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On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D [PDF]
Theoretical and Applied Mechanics, 2017 The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the Oregonator model are derived using the method of Darboux polynomials.
Esen Oğul +2 more
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The solution of some persistent $p : -q$ resonant center problems
Electronic Journal of Qualitative Theory of Differential Equations, 2018 The notion of $p:-q$ resonant center was introduced recently and studied by several authors. In this paper we generalize the notion of a persistent center to a persistent $p:-q $ resonant center and find conditions for existence of a persistent $p:-q ...
Maja Zulj +2 more
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Integrability of Nonholonomic Heisenberg Type Systems [PDF]
, 2016 We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical $r ...
Grigoryev, Yury A. +2 more
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Darboux transformations for SUSY integrable systems [PDF]
, 2007 13 pages. LaTeX209 with LamuPhys and EPSF packages, 3 figures. Contribution to the proceedings of the "Integrable Models and Supersymmetry" meeting held at Chicago on July ...
Liu, Q. P., Manas, Manuel
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On a class of Darboux-integrable semidiscrete equations
Advances in Difference Equations, 2017 We consider a classification problem for Darboux-integrable hyperbolic semidiscrete equations. In particular, we obtain a complete description for a special class of equations admitting four-dimensional characteristic x-rings and two-dimensional ...
Kostyantyn Zheltukhin +2 more
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From the Birkhoff-Gustavson normalization to the Bertrand-Darboux integrability condition
, 2000 The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the Birkhoff-Gustavson(BG)-normalization: By solving an inverse problem of the BG-normalization on computer algebra, it is
Arnold V I +17 more
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Explicit Solutions and Conservation Laws for a New Integrable Lattice Hierarchy
Complexity, 2019 An integrable lattice hierarchy is derived on the basis of a new matrix spectral problem. Then, some properties of this hierarchy are shown, such as the Liouville integrability, the bi-Hamiltonian structure, and infinitely many conservation laws.
Qianqian Yang, Qiulan Zhao, Xinyue Li
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