Results 1 to 10 of about 6,078 (188)

Darboux Integrals for Schrödinger Planar Vector Fields via Darboux Transformations [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2012
In this paper we study the Darboux transformations of planar vector fields of Schrödinger type. Using the isogaloisian property of Darboux transformation we prove the ''invariance'' of the objects of the ''Darboux theory of integrability''. In particular,
Primitivo B. Acosta-Humánez, Chara Pantazi   +1 more
doaj   +10 more sources

Darboux integration of [PDF]

Physics Letters A, 2001
Abstract A Darboux-type method of solving a class of nonlinear von Neumann equations i ρ =[H,f(ρ)] is developed. An explicit construction demonstrates that self-scattering solutions are a generic property of the nonlinearities considered. A solution for an infinite-dimensional case is presented.
Nikolai V. Ustinov, Marek Czachor, Maciej Kuna, Sergiej B. Leble   +3 more
openaire   +4 more sources

Lotka–Volterra lattice system: N-fold Darboux transformation, the corresponding integrable lattice family and bi-Hamiltonian structure

Partial Differential Equations in Applied Mathematics, 2023
An one-fold Darboux transformation for the Lotka–Volterra lattice system is first established using a proper gauge transformation matrix. Then, as a result of the N times one-fold Darboux transformation, the corresponding N-fold Darboux transformation of
Rong-Wu Lu, Xi-Xiang Xu
doaj   +1 more source

Explicit solutions of rational integrable differential-difference equations

Partial Differential Equations in Applied Mathematics, 2022
The rational integrable differential-difference equations are proposed from a different discrete spectral problem. We proved the Liouville integrability of rational integrable differential-difference equations by deriving its bi-Hamiltonian structures ...
Qiulan Zhao, Muhammad Arham Amin
doaj   +1 more source

Liouvillian Integrability Versus Darboux Polynomials [PDF]

Qualitative Theory of Dynamical Systems, 2016
Agraïments: FEDER/UNAB10-4E-378. The second author is supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. The third author is partially supported by NNSF of China grant number 11271252, by RFDP of Higher Education of China grant number 20110073110054, and by ...
Llibre, Jaume, Valls, Clàudia, Zhang, Xiang   +2 more
openaire   +6 more sources

Geometry, integrability and bifurcation diagrams of a family of quadratic differential systems as application of the Darboux theory of integrability

Electronic Journal of Qualitative Theory of Differential Equations, 2021
During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research.
Regilene Oliveira, Dana Schlomiuk, Ana Maria Travaglini, Claudia Valls   +3 more
doaj   +1 more source

Darboux integrability of a hyperjerk memristive system

Zanco Journal of Pure and Applied Sciences, 2023
In this work, we investigate the following novel four-dimensional dynamical memristive system (see, (Prousalis et al., 2017)) This system, in a certain area of the parameter space, exhibits hyper-jerk dynamics and a line of singularities passing ...
Niazy Hady Hussein ,Soran Mohammed Khudur
doaj   +1 more source

Isometric embedding and Darboux integrability [PDF]

Geometriae Dedicata, 2019
Given a smooth 2-dimensional Riemannian or pseudo-Riemannian manifold $(M, \boldsymbol{g})$ and an ambient 3-dimensional Riemannian or pseudo-Riemannian manifold $(N, \boldsymbol{h})$, one can ask under what circumstances does the exterior differential system $\mathcal{I}$ for the isometric embedding $M\hookrightarrow N$ have particularly nice ...
J. N. Clelland, T. A. Ivey, N. Tehseen, P. J. Vassiliou   +3 more
openaire   +4 more sources

On integrability and cyclicity of cubic systems

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper we study the integrability of a few families of the complex cubic system. We have obtained necessary and sufficient conditions for existence of a local analytic first integral.
Maša Dukarić
doaj   +1 more source

Darboux Integrability of a Generalized 3D Chaotic Sprott ET9 System

مجلة بغداد للعلوم, 2022
In this paper, the first integrals of Darboux type of the generalized Sprott ET9 chaotic system will be studied. This study showed that the system has no polynomial, rational, analytic and Darboux first integrals for any value of .
Adnan Ali Jalal, Azad I. Amen, Nejmaddin A. Sulaiman   +2 more
doaj   +1 more source