From AKNS to derivative NLS hierarchies via deformations of associative products

Abstract

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.

arXiv comment22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of section 2 rewritten, taking account of previously overlooked references. To appear in J. Physics A: Math. Gen

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Cited by in corpus (9)

• Systematic method of generating new integrable systems via inverse Miura maps
• New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems
• Burgers and KP hierarchies: A functional representation approach
• Functional representation of the negative AKNS hierarchy
• Exact solutions of multicomponent nonlinear Schrödinger equations under general plane-wave boundary conditions
• Solutions of matrix NLS systems and their discretisations: A unified treatment
• On a new integrable discretization of the derivative nonlinear Schrödinger (Chen-Lee-Liu) equation
• Bäcklund transformations between the AKNS and DNLS hierarchies
• Functional representation of the negative DNLS hierarchy