Results 41 to 50 of about 863 (58)

UC and BUC plane partitions

European Physical Journal C: Particles and Fields
This paper is concerned with the investigation of UC and BUC plane partitions based upon the fermion calculus approach. We construct generalized the vertex operators in terms of free charged fermions and neutral fermions and present the interlacing ...
Shengyu Zhang, Zhaowen Yan
doaj   +1 more source

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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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
core   +1 more source

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
core   +2 more sources

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
core   +1 more source

An invariant in shock clustering and Burgers turbulence

, 2012
1-D scalar conservation laws with convex flux and Markov initial data are now known to yield a completely integrable Hamiltonian system. In this article, we rederive the analogue of Loitsiansky's invariant in hydrodynamic turbulence from the perspective ...
Burgers J M, Burgers J M, Burgers J M, Burgers J M, Burgers J M, Carraro L, Kolmogorov A N, Loitsianskii L G, Menon G, Ravi Srinivasan, Woyczyński W A   +10 more
core   +1 more source

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
core   +1 more source

A bi-Hamiltonian approach to the sine-Gordon and Liouville hierarchies

, 2003
In this paper we study the sine-Gordon and the Liouville hierarchies in laboratory coordinates from a bi-Hamiltonian point of view. Besides the well-known local structure these hierarchies possess a second compatible non-local Poisson structure.Comment ...
Lorenzoni, Paolo
core   +3 more sources

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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Recursion operator for the IGSG equation

, 2006
In this paper we find the inverse and direct recursion operator for the intrinsic generalized sine-Gordon equation in any number $n > 2$ of independent variables.
Marvan, M., Pobořil, M.
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