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The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups
Variational formulation of commuting Hamiltonian flows: Multi-time Lagrangian 1-forms
1. | Institut für Mathematik, MA 7-2, Technische Universität Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany |
References:
[1] |
V. E. Adler, A. I. Bobenko and Yu. B. Suris, Classification of integrable equations on quad-graphs. The consistency approach,, Commun. Math. Phys., 233 (2003), 513.
|
[2] |
A. I. Bobenko and Yu. B. Suris, Integrable systems on quad-graphs,, International Mathematics Research Notices, 2002 (2002), 573.
doi: 10.1155/S1073792802110075. |
[3] |
A. I. Bobenko and Yu. B. Suris, "Discrete Differential Geometry. Integrable Structure,", Graduate Studies in Mathematics, (2008).
|
[4] |
A. I. Bobenko and Yu. B. Suris, On the Lagrangian structure of integrable quad-equations,, Letters in Mathematical Physics, 92 (2010), 17.
doi: 10.1007/s11005-010-0381-9. |
[5] |
R. Boll, M. Petrera and Yu. B. Suris, Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Toda-type systems,, Journal of Physics A: Mathematical and Theoretical, 46 (2013).
doi: 10.1088/1751-8113/46/27/275204. |
[6] |
V. B. Kuznetsov and E. K. Sklyanin, On Bäcklund transformations for many-body systems,, Journal of Physics A: Mathematical and General, 31 (1998), 2241.
doi: 10.1088/0305-4470/31/9/012. |
[7] |
S. B. Lobb and F. W. Nijhoff, Lagrangian multiforms and multidimensional consistency,, Journal of Physics A: Mathematical and Theoretical, 42 (2009).
doi: 10.1088/1751-8113/42/45/454013. |
[8] |
S. B. Lobb and F. W. Nijhoff, Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy,, Journal of Physics A: Mathematical and Theoretical, 43 (2010).
doi: 10.1088/1751-8113/43/7/072003. |
[9] |
S. B. Lobb, F. W. Nijhoff and G. R. W. Quispel, Lagrangian multiform structure for the lattice KP system,, Journal of Physics A: Mathematical and Theoretical, 42 (2009).
doi: 10.1088/1751-8113/42/47/472002. |
[10] |
J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials,, Communications in Mathematical Physics, 139 (1991), 217.
doi: 10.1007/BF02352494. |
[11] |
F. W. Nijhoff, Lax pair for the Adler (lattice Krichever-Novikov) system,, Physics Letters A, 297 (2002), 49.
doi: 10.1016/S0375-9601(02)00287-6. |
[12] |
J. Roels and A. Weinstein, Functions whose Poisson brackets are constants,, Journal of Mathematical Physics, 12 (1971), 1482.
doi: 10.1063/1.1665760. |
[13] |
N. Román-Roy, Á.M. Rey, M. Salgado and S. Vilariño, On the $k$-symplectic, $k$-cosymplectic and multisymplectic formalisms of classical field theories,, J. Geom. Mech., 3 (2011), 113.
|
[14] |
Yu. B. Suris, "The Problem of Integrable Discretization: Hamiltonian Approach,", Progress in Mathematics, (2003).
doi: 10.1007/978-3-0348-8016-9. |
[15] |
M. Wadati and M. Toda, Bäcklund transformation for the exponential lattice,, Journal of the Physical Society of Japan, 39 (1975), 1196.
doi: 10.1143/JPSJ.39.1196. |
[16] |
S. Yoo-Kong, S. Lobb and F. W. Nijhoff, Discrete-time Calogero-Moser system and Lagrangian 1-form structure,, Journal of Physics A: Mathematical and Theoretical, 44 (2011).
doi: 10.1088/1751-8113/44/36/365203. |
show all references
References:
[1] |
V. E. Adler, A. I. Bobenko and Yu. B. Suris, Classification of integrable equations on quad-graphs. The consistency approach,, Commun. Math. Phys., 233 (2003), 513.
|
[2] |
A. I. Bobenko and Yu. B. Suris, Integrable systems on quad-graphs,, International Mathematics Research Notices, 2002 (2002), 573.
doi: 10.1155/S1073792802110075. |
[3] |
A. I. Bobenko and Yu. B. Suris, "Discrete Differential Geometry. Integrable Structure,", Graduate Studies in Mathematics, (2008).
|
[4] |
A. I. Bobenko and Yu. B. Suris, On the Lagrangian structure of integrable quad-equations,, Letters in Mathematical Physics, 92 (2010), 17.
doi: 10.1007/s11005-010-0381-9. |
[5] |
R. Boll, M. Petrera and Yu. B. Suris, Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Toda-type systems,, Journal of Physics A: Mathematical and Theoretical, 46 (2013).
doi: 10.1088/1751-8113/46/27/275204. |
[6] |
V. B. Kuznetsov and E. K. Sklyanin, On Bäcklund transformations for many-body systems,, Journal of Physics A: Mathematical and General, 31 (1998), 2241.
doi: 10.1088/0305-4470/31/9/012. |
[7] |
S. B. Lobb and F. W. Nijhoff, Lagrangian multiforms and multidimensional consistency,, Journal of Physics A: Mathematical and Theoretical, 42 (2009).
doi: 10.1088/1751-8113/42/45/454013. |
[8] |
S. B. Lobb and F. W. Nijhoff, Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy,, Journal of Physics A: Mathematical and Theoretical, 43 (2010).
doi: 10.1088/1751-8113/43/7/072003. |
[9] |
S. B. Lobb, F. W. Nijhoff and G. R. W. Quispel, Lagrangian multiform structure for the lattice KP system,, Journal of Physics A: Mathematical and Theoretical, 42 (2009).
doi: 10.1088/1751-8113/42/47/472002. |
[10] |
J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials,, Communications in Mathematical Physics, 139 (1991), 217.
doi: 10.1007/BF02352494. |
[11] |
F. W. Nijhoff, Lax pair for the Adler (lattice Krichever-Novikov) system,, Physics Letters A, 297 (2002), 49.
doi: 10.1016/S0375-9601(02)00287-6. |
[12] |
J. Roels and A. Weinstein, Functions whose Poisson brackets are constants,, Journal of Mathematical Physics, 12 (1971), 1482.
doi: 10.1063/1.1665760. |
[13] |
N. Román-Roy, Á.M. Rey, M. Salgado and S. Vilariño, On the $k$-symplectic, $k$-cosymplectic and multisymplectic formalisms of classical field theories,, J. Geom. Mech., 3 (2011), 113.
|
[14] |
Yu. B. Suris, "The Problem of Integrable Discretization: Hamiltonian Approach,", Progress in Mathematics, (2003).
doi: 10.1007/978-3-0348-8016-9. |
[15] |
M. Wadati and M. Toda, Bäcklund transformation for the exponential lattice,, Journal of the Physical Society of Japan, 39 (1975), 1196.
doi: 10.1143/JPSJ.39.1196. |
[16] |
S. Yoo-Kong, S. Lobb and F. W. Nijhoff, Discrete-time Calogero-Moser system and Lagrangian 1-form structure,, Journal of Physics A: Mathematical and Theoretical, 44 (2011).
doi: 10.1088/1751-8113/44/36/365203. |
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