%0 Journal Article
%A Jaulent, Marcel
%A Manna, Miguel A.
%A Martínez Alonso, Luis
%T Multiseries Lie-groups and asymptotic modules for characterizing and solving integrable models
%D 1989
%@ 0022-2488
%U https://hdl.handle.net/20.500.14352/59833
%X 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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