City Research Online

Time-delay and reality conditions for complex solitons

Cen, J., Correa, F. & Fring, A. (2017). Time-delay and reality conditions for complex solitons. Journal of Mathematical Physics, 58(3), article number 032901. doi: 10.1063/1.4978864

Abstract

We compute lateral displacements and time-delays for scattering processes of complex multi-soliton solutions of the Korteweg de-Vries equation. The resulting expressions are employed to explain the precise distinction between solutions obtained from different techniques, Hirota’s direct method and a superposition principle based on Bäcklund transformations. Moreover they explain the internal structures of degenerate compound multi-solitons previously constructed. Their individual one-soliton constituents are time-delayed when scattered amongst each other. We present generic formulae for these time-dependent displacements. By recalling Gardner’s transformation method for conserved charges, we argue that the structure of the asymptotic behaviour resulting from the integrability of the model together with its PT-symmetry ensures the reality of all of these charges, including in particular the mass, the momentum, and the energy.

Publication Type: Article
Additional Information: This is the accepted manuscript for Cen, J., Correa, F. & Fring, A. (2017). Time-delay and reality conditions for complex solitons. Journal of Mathematical Physics, 58(3), 032901. The published version is available on AIP website at https://dx.doi.org/10.1063/1.4978864.
Publisher Keywords: Particle scattering, Multiple scattering, Time dependent material structure, Integrable systems, Semiclassical theories
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
[thumbnail of TimeDelay.pdf]
Preview
Text - Accepted Version
Download (587kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login