- 10.1080/14029251.2020.1683963How to use a DOI?
- nonlinear wave equations; solitons; quaternions; coquaternions; octonions
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.
- © 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
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 -