Journal of Nonlinear Mathematical Physics

Volume 20, Issue 4, December 2013, Pages 606 - 622

Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

Authors
Oleksiy O. Vakhnenko
Quantum Electronics Department, Bogolyubov Institute for Theoretical Physics, 14-B Metrologichna Street Kyïv, 03680-UA, Ukraïna, vakhnenko@bitp.kiev.ua
Received 19 September 2013, Accepted 17 November 2013, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2013.865827How to use a DOI?
Keywords
integrable nonlinear system, local conservation laws, 𝒫𝒯-symmetry, beam-plasma oscillations
Abstract

The new type of third-order spectral operator suitable to generate new multifield semidiscrete nonlinear systems with two coupling parameters in the framework of zero-curvature equation is proposed. The evolution operator corresponding to the first integrable system in an infinite hierarchy is explicitly recovered and the general form of first integrable system is isolated. The generalized procedure for the direct recursive development of infinite hierarchy of local conservation laws is presented and several lowest local conservation laws and local conserved densities are found. The reduction to the real field amplitudes in general system with unfixed sampling functions is made and the symmetric parametrization of field amplitudes allowing to exclude the redundant field function and to resolve the problem of sampling fixation for the particular realization of reduced integrable system is considered. This parametrization gives rise to the four field nonlinear model which in certain intervals of adjustable coupling parameter could serve as a semidiscrete analogy to the beam-plasma interaction system.

Copyright
© 2013 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 4
Pages
606 - 622
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.865827How to use a DOI?
Copyright
© 2013 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Oleksiy O. Vakhnenko
PY  - 2021
DA  - 2021/01
TI  - Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry
JO  - Journal of Nonlinear Mathematical Physics
SP  - 606
EP  - 622
VL  - 20
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.865827
DO  - https://doi.org/10.1080/14029251.2013.865827
ID  - Vakhnenko2021
ER  -