From AKNS to derivative NLS hierarchies via deformations of associative products

Details From AKNS to derivative NLS hierarchies via deformations of associative products From AKNS to derivative NLS hierarchies via deformations of associative products

2006-03-23

arxiv.org/abs/nlin/0603048v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of se

Scientific paper

10.1088/0305-4470/39/45/010

Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed method to obtain 'functional representations' can be applied. We actually consider hierarchies with dependent variables in any (possibly noncommutative) associative algebra, e.g., an algebra of matrices of functions. This also covers the case of hierarchies of coupled DNLS equations.

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