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Multiseries Lie-groups and asymptotic modules for characterizing and solving integrable models

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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


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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.


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©1989 American Institute of Physics.
M. M. and L. M. A. wish to thank Professor P. C. Sabatier and the Laboratoire de Physique Mathematique de Montpellier for their warm hospitality.

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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