Results 51 to 60 of about 936 (79)

A 3-component extension of the Camassa-Holm hierarchy

, 2006
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a 3-component extension of ...
B. Fuchssteiner, B. Khesin, E.G. Reyes, G. Falqui, H. McKean, J.E. Marsden, L.A. Dickey, Laura Fontanelli, M. Pedroni, Marco Pedroni, P. Casati, P. Casati, P. Casati, P. Libermann, P. Lorenzoni, Paolo Lorenzoni, R. Beals, R. Beals, R. Camassa, S. Abenda, S. Liu, V.E. Zakharov, V.G. Drinfeld   +22 more
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Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov--Burgers system revisited

, 2008
We consider the Burgers-type system studied by Foursov, w_t &=& w_{xx} + 8 w w_x + (2-4\alpha)z z_x, z_t &=& (1-2\alpha)z_{xx} - 4\alpha z w_x + (4-8\alpha)w z_x - (4+8\alpha)w^2 z + (-2+4\alpha)z^3, (*) for which no recursion operator or master symmetry
A. Sergyeyev, A. Sergyeyev, A. Sergyeyev, A.S. Fokas, A.S. Fokas, A.V. Bocharov, A.V. Mikhailov, Artur Sergyeyev, B. Kruglikov, B. Kruglikov, B.G. Konopelchenko, F. Beukers, F. Calogero, G.A. Guthrie, I. Dorfman, I.S. Krasil’shchik, I.S. Krasil’shchik, I.S. Krasil’shchik, I.S. Krasil’shchik, J.A. Sanders, K. Foltinek, M. Błaszak, M. Marvan, M.V. Foursov, N.H. Ibragimov, P.H. Kamp van der, P.J. Olver, P.J. Olver, R.O. Popovych, R.Z. Zhdanov, S.I. Svinolupov, T. Tsuchida   +31 more
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Integrable Anisotropic Evolution Equations on a Sphere

, 2005
V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the n-dimensional sphere. The main result is a complete classification of such equations.
Balakhnev, Maxim Ju., Meshkov, Anatoly G.   +1 more
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Additional symmetries of constrained CKP and BKP hierarchies

, 2010
The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction $\{\Phi_i,\Psi_i \}$ are presented explicitly ...
A. Alexandrov, A. Mironov, A. Morozov, A. Y. Orlov, B. G. Konopelchenko, E. Date, E. Date, H. Aratyn, H. Aratyn, H. F. Shen, I. Loris, I. Loris, I. Loris, J. S. He, J. S. He, JingSong He, JiPeng Cheng, K. Takasaki, KeLei Tian, L. A. Dickey, L. A. Dickey, L. A. Dickey, M. Adler, M. Adler, M. H. Tu, P. Moerbke van, W. X. Ma, W. X. Ma, W. X. Ma, Y. Cheng, Y. Cheng, Yi Cheng   +31 more
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Soliton solution of the osmosis K(2, 2) equation

, 2009
In this Letter, by using the bifurcation method of dynamical systems, we obtain the analytic expressions of soliton solution of the osmosis K(2, 2) equation.Comment: 8 ...
Biswas, Jiangbo Zhou, Lixin Tian, Luo, Rosenau, Wazwaz, Wazwaz, Wazwaz, Xu, Yan, Zhu   +10 more
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Canonically Conjugate Variables for the μCH Equation [PDF]

, 2012
2010 Mathematics Subject Classification: 35Q35, 37K10.We consider the μCH equation which arises as an asymptotic rotator equation in a liquid crystal with a preferred direction if one takes into account the reciprocal action of dipoles on themselves ...
Christov, Ognyan
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Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics

, 2017
We study decay of small solutions of the Born-Infeld equation in 1+1 dimensions, a quasilinear scalar field equation modeling nonlinear electromagnetism, as well as branes in String theory and minimal surfaces in Minkowski space-times.
Alejo, Miguel A., Muñoz, Claudio
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A q-analogue of gl_3 hierarchy and q-Painleve VI

, 2006
A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI equation proposed by Jimbo and Sakai ...
Conte R Grundland A M Musette M, Hahn W, Kakei S Kikuchi T, Mazzocco M, Saburo Kakei, Tetsuya Kikuchi, Ueno K, Wu Z Y, Zhang C   +8 more
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Algebraic theories of brackets and related (co)homologies

, 2009
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.Comment:
A. Frölicher, A. Frölicher, A. Lichnerowicz, A. Nijenhuis, A. Nijenhuis, A. Nijenhuis, A. Vinogradov, A. Vinogradov, A. Vinogradov, A. Vinogradov, A.M. Vinogradov, A.V. Bocharov, F. Magri, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, I. Krasil’shchik, Iosif Krasil’shchik, J.-L. Brylinski, J.A. Schouten, J.A. Schouten, P. Kersten, V. Lychagin   +26 more
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The Additional Symmetries for the BTL and CTL Hierarchies

, 2011
The Toda lattice (TL) hierarchy was first introduced by K.Ueno and K.Takasaki in \cite{uenotaksasai} to generalize the Toda lattice equations\cite{toda}. Along the work of E. Date, M. Jimbo, M. Kashiwara and T.
Date E., Jingsong He, Jipeng Cheng, Kelei Tian, Ueno K., van Moerbeke P.   +5 more
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