Results 21 to 30 of about 6,078 (188)

A Comprehensive Study of the Complex mKdV Equation through the Singular Manifold Method

Mathematics, 2023
In this paper, we introduce a modification of the Singular Manifold Method in order to derive the associated spectral problem for a generalization of the complex version of the modified Korteweg–de Vries equation.
Paz Albares, Pilar G. Estévez
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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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A Family of Integrable Different-Difference Equations, Its Hamiltonian Structure, and Darboux-Bäcklund Transformation

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, Giacomini, Hector, Giné, Jaume, Llibre, Jaume   +3 more
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Differential Calculi on Associative Algebras and Integrable Systems

, 2020
After an introduction to some aspects of bidifferential calculus on associative algebras, we focus on the notion of a "symmetry" of a generalized zero curvature equation and derive Backlund and (forward, backward and binary) Darboux transformations from ...
A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Dimakis, A Sitarz, C Rogers, D-J Zhang, E Brezin, F Magri, F Magri, G Chavchanidze, G Tondo, J Grifone, J Hietarinta, JT Hartwig, LJ Mason, M Crampin, M Crampin, O Chvartatskyi, P Lorenzoni, P Lorenzoni, VA Marchenko, VK Mel’nikov, Y Kosmann-Schwarzbach   +30 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, Brigita Ferčec, Matej Mencinger   +2 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, Choudhury Ghose Anindya, Guha Partha   +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, Natalya Zheltukhina, Ergun Bilen   +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, Chekanov N A, Cushman R, Darboux G, Goldstein H, Grosche C, Kummer M, Moser J K, Perelomov A M, Spivak M, Uwano Y, Uwano Y, Uwano Y, Uwano Y, Uwano Y, Whittaker E T, Yamaguchi Y Y, Yoshio Uwano   +17 more
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