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arXiv · 1608.01691

Time-delay and reality conditions for complex solitons

Julia Cen·Francisco Correa·Andreas Fring
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Abstract

We compute lateral displacements and time-delays for a 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 Baecklund 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 ensure the reality of all of these charges, including in particular the mass, the momentum and the energy.

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Julia Cen, Francisco Correa, Andreas Fring. 2016-08-04. Time-delay and reality conditions for complex solitons. https://doi.org/10.1063/1.4978864

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