City Research Online

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

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