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Jaulent, Marcel and Manna, Miguel A. and Martínez Alonso, Luis
(1989)
*Multiseries Lie-groups and asymptotic modules for characterizing and solving integrable models.*
Journal of mathematical physics, 30
(8).
pp. 1662-1673.
ISSN 0022-2488

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Official URL: http://dx.doi.org/10.1063/1.528251

## Abstract

A multiseries integrable model (MSIM) is defined as a family of compatible flows on an infinite-dimensional Lie group of N-tuples of formal series around N given poles on the Riemann sphere. Broad classes of solutions to a MSIM are characterized through modules over rings of rational functions, called asymptotic modules. Possible ways for constructing asymptotic modules are Riemann-Hilbert and (j problems. When MSIM's are written in terms of the "group coordinates," some of them can be "contracted" into standard integrable models involving a small number of scalar functions only. Simple contractible MSIM's corresponding to one pole, yield the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy. Two-pole contractible MSIM's are exhibited, which lead to a hierarchy of solvable systems of nonlinear differential equations consisting of (2 + 1 )-dimensional evolution equations and of quite strong differential constraints.

Item Type: | Article |
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Additional Information: | ©1989 American Institute of Physics. |

Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |

ID Code: | 34521 |

Deposited On: | 03 Dec 2015 16:36 |

Last Modified: | 10 Dec 2018 15:10 |

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