Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 1, October 2019, Pages 17 - 35

Multicomplex solitons

Authors
Julia Cen
Department of Mathematics, City, University of London Northampton Square, London EC1V 0HB, UK,julia.cen.1@city.ac.uk
Andreas Fring
Department of Mathematics, City, University of London Northampton Square, London EC1V 0HB, UK,a.fring@city.ac.uk
Received 7 December 2018, Accepted 11 June 2019, Available Online 25 October 2019.
DOI
10.1080/14029251.2020.1683963How to use a DOI?
Keywords
nonlinear wave equations; solitons; quaternions; coquaternions; octonions
Abstract

We discuss integrable extensions of real nonlinear wave equations with multi-soliton solutions, to their bicomplex, quaternionic, coquaternionic and octonionic versions. In particular, we investigate these variants for the local and nonlocal Korteweg-de Vries equation and elaborate on how multi-soliton solutions with various types of novel qualitative behaviour can be constructed. Corresponding to the different multicomplex units in these extensions, real, hyperbolic or imaginary, the wave equations and their solutions exhibit multiple versions of antilinear or 𝒫𝒯-symmetries. Utilizing these symmetries forces certain components of the conserved quantities to vanish, so that one may enforce them to be real. We find that symmetrizing the noncommutative equations is equivalent to imposing a 𝒫𝒯-symmetry for a newly defined imaginary unit from combinations of imaginary and hyperbolic units in the canonical representation.

Copyright
© 2020 The Authors. Published by Atlantis 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
17 - 35
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1683963How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis 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

risenwbib
TY  - JOUR
AU  - Julia Cen
AU  - Andreas Fring
PY  - 2019
DA  - 2019/10/25
TI  - Multicomplex solitons
JO  - Journal of Nonlinear Mathematical Physics
SP  - 17
EP  - 35
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683963
DO  - 10.1080/14029251.2020.1683963
ID  - Cen2019
ER  -