Relativistic DNLS and Kaup-Newell Hierarchy

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....

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Bibliographic Details
Published inarXiv.org
Main Authors Pashaev, Oktay K, Lee, Jyh-Hao
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 25.07.2017
Subjects
Integral calculus
Integral equations
Mathematics - Mathematical Physics
Physics - Exactly Solvable and Integrable Systems
Physics - Mathematical Physics
Relativism
Relativistic effects
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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.
ISSN:2331-8422
DOI:10.48550/arxiv.1704.04078