Results 1 to 10 of about 178 (161)
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 +1 more
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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 ...
Xiang Zhang, Jaume Llibre
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Liouvillian Integrability Versus Darboux Polynomials [PDF]
Qualitative Theory of Dynamical Systems, 2016 In this note we provide a sufficient condition on the existence of Darboux polynomials of polynomial differential systems via existence of Jacobian multiplier or of Liouvillian first integral and a degree condition among different components of the system. As an application of our main results we prove that the Liénard polynomial differential system x
Xiang Zhang +2 more
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On the Darboux integrability of the Hindmarsh–Rose burster [PDF]
Acta Mathematica Sinica, English Series, 2017 We study the HindmarshRose burster which can be described by the differential system x?=y?x3+bx2+I?z,y?=1?5x2?y,z?=?(s(x?x0)?z), where b, I, ?, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters.
Claudia Valls +2 more
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Darboux Integrability Of the Biological System
Al-Rafidain Journal of Computer Sciences and MathematicsIn the given paper, we investigate the integrability of a mathematical model of a 3D biological system. Our results show that the system admits a polynomial first integrals for some parameters, an invariant algebraic surface with an exponential factor ...
Zakariya Hashem Ali +1 more
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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
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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 +3 more
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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
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On the classification of Darboux integrable chains [PDF]
Journal of Mathematical Physics, 2008 We study a differential-difference equation of the form tx(n+1)=f(t(n),t(n+1),tx(n)) with unknown t=t(n,x) depending on x and n. The equation is called a Darboux integrable if there exist functions F (called an x-integral) and I (called an n-integral), both of a finite number of variables x,t(n),t(n±1),t(n±2),…,tx(n),txx(n),…, such that DxF=0 and DI=I,
Habibullin, I. +2 more
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