Results 91 to 100 of about 6,078 (188)

Non-integrability of the Armbruster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory [PDF]

, 2017
We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases.
Acosta-Humánez, P., Alvarez-Ramírez, M., Stuchi, T.   +2 more
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Discrete asymptotic nets and W-congruences in Plucker line geometry

, 2000
The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric.
Adam Doliwa, Bobenko, Bogdanov, Doliwa, Doliwa, Doliwa, Doliwa, Doliwa, Doliwa, Ernst, Ganzha, Hirota, Hirota, Klein, Konopelchenko, Konopelchenko, Krichever, Lelieuvre, Levi, Levi, Mañas, Moutard, Nimmo, Plebański, Plücker, Schief   +25 more
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First integrals in a cubic differential system with one invariant straight line and one invariant cubic

Acta et Commentationes: Ştiinţe Exacte şi ale Naturii
In this paper we find conditions for a singular point O(0, 0) of a center or a focus type to be a center, in a cubic differential system with one invariant straight line and one invariant cubic.
Dumitru Cozma
doaj   +1 more source

Darboux Transformations of Bispectral Quantum Integrable Systems

Letters in Mathematical Physics, 1999
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to ...
Horozov, Emil, Kasman, Alex
openaire   +3 more sources

Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

, 2001
It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings ...
Ablowitz M J, Ahlfors L V, Askwith E H, B G Konopelchenko, Bers L, Bobenko A I, Bobenko A I, Bobenko A I, Bobenko A I, Bogdanov L V, Bogdanov L V, Brannan D A, Caraman P, Clifford W K, Darboux G, Dijkgraaf R, Dryuma V S, Guggenheimer H, Jimbo M, Kadomtsev B B, Lehto O, Lester J A, Longuet-Higgins M S, Matveev V B, Miwa T, Morley F, Morozov A, Nijhoff F, Nijhoff F W, Nijhoff F W, Pedoe D, Reshetnyak Yu G, Schramm O, Shiota T, Steiner J, Vuorinen M (ed), W K Schief, Wallace W ('Scoticus'), Zakharov V E, Zakharov V E, Ziegenbein P   +40 more
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On integrable reductions of two-dimensional Toda-type lattices

Partial Differential Equations in Applied Mathematics
The article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the nonlinear Schrödinger type.
I.T. Habibullin, A.U. Sakieva
doaj   +1 more source

Relationships between Darboux Integrability and Limit Cycles for a Class of Able Equations [PDF]

Journal of Sciences, Islamic Republic of Iran, 2006
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i.
doaj  

Integral transformation and Darboux transformation

, 2009
We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation of monodromy with respect to the transformations.
openaire   +2 more sources

SYMMETRIES AND LAX INTEGRABILITY OF THE GENERALIZED PROUDMAN-JOHNSON EQUATION

Научный вестник МГТУ ГА, 2017
We study local symmetries of the generalized Proudman-Johnson equation. Symmetries of a partial differential equation may be used to find its invariant solutions.
O. I. Morozov
doaj  

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation. [PDF]

Sci Rep, 2023
Fan C, Li L, Yu F.
europepmc   +1 more source