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 SIGMA, 2017, Volume 13, 058, 13 pages (Mi sigma1258)

Relativistic DNLS and Kaup–Newell Hierarchy

Oktay K. Pashaeva, Jyh-Hao Leeb

a Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430, Turkey
b Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan

Abstract: 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.

Keywords: Kaup–Newell hierarchy; relativistic DNLS; $q$-calculus; recursion operator.

 Funding Agency Grant Number Scientific and Technological Research Council of Turkey (TÜBITAK) TBAG-116F206 Izmir Institute of Technology, Turkey This work was partially supported by Izmir Institute of Technology, Turkey, and Institute of Mathematics, Academia Sinica, Taiwan. The work of O.K.P. was supported by the Scientific and Technological Research Council of Turkey (TUBITAK), Grant No: TBAG-116F206.

DOI: https://doi.org/10.3842/SIGMA.2017.058

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MSC: 35Q55; 37K10
Received: April 14, 2017; in final form July 18, 2017; Published online July 25, 2017
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Citation: Oktay K. Pashaev, Jyh-Hao Lee, “Relativistic DNLS and Kaup–Newell Hierarchy”, SIGMA, 13 (2017), 058, 13 pp.

Citation in format AMSBIB
\Bibitem{PasLee17} \by Oktay~K.~Pashaev, Jyh-Hao~Lee \paper Relativistic DNLS and Kaup--Newell Hierarchy \jour SIGMA \yr 2017 \vol 13 \papernumber 058 \totalpages 13 \mathnet{http://mi.mathnet.ru/sigma1258} \crossref{https://doi.org/10.3842/SIGMA.2017.058} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000406498000001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85026820848} 

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This publication is cited in the following articles:
1. A. Biswas, M. Ekici, A. Sonmezoglu, R. T. Alqahtani, “Sub-pico-second chirped optical solitons in mono-mode fibers with Kaup-Newell equation by extended trial function method”, Optik, 168 (2018), 208–216
2. A. Biswasa, Ya. Yildirim, E. Yasar, Q. Zhou, S. P. Moshokoa, M. Belic, “Sub pico-second pulses in mono-mode optical fibers with Kaup-Newell equation by a couple of integration schemes”, Optik, 167 (2018), 121–128
3. S. Arshed, A. Biswas, M. Abdelaty, Q. Zhou, S. P. Moshokoa, M. Belic, “Sub pico-second chirp-free optical solitons with Kaup-Newell equation using a couple of strategic algorithms”, Optik, 172 (2018), 766–771
4. Jia T.-T., Gao Y.-T., Feng Yu.-J., Hu L., Su J.-J., Li L.-Q., Ding C.-C., “On the Quintic Time-Dependent Coefficient Derivative Nonlinear Schrodinger Equation in Hydrodynamics Or Fiber Optics”, Nonlinear Dyn., 96:1 (2019), 229–241
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