From AKNS to derivative NLS hierarchies via deformations of associative products

Dimakis, Aristophanes; Müller-Hoissen, Folkert

doi:10.1088/0305-4470/39/45/010

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From AKNS to derivative NLS hierarchies via deformations of associative products

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Müller-Hoissen, Folkert
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Dimakis, A., & Müller-Hoissen, F. (2006). From AKNS to derivative NLS hierarchies via deformations of associative products. Journal of Physics A: Mathematical and General, 39, 14015-14033. doi:10.1088/0305-4470/39/45/010.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-14A1-5

Abstract

Using deformations of associative products, derivative nonlinear Schrödinger (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 derivative NLS equations.