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Relativistic DNLS and Kaup-Newell hierarchy. (English) Zbl 1372.35286

Summary: By the recursion operator of the Kaup-Newell hierarchy we construct the relativistic derivative NLS (RDNLS) equation and the corresponding Lax pair. In the nonrelativistic limit \(c \rightarrow \infty\) it reduces to DNLS equation and preserves integrability at any order of relativistic corrections. The compact explicit representation of the linear problem for this equation becomes possible due to notions of the \(q\)-calculus with two bases, one of which is the recursion operator, and another one is the spectral parameter.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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