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Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation

Cen, J. and Fring, A. ORCID: 0000-0002-7896-7161 (2019). Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation. Physica D: Nonlinear Phenomena, 397, pp. 17-24. doi: 10.1016/j.physd.2019.05.005

Abstract

We construct all higher order conserved charges from a general two-dimensional zero curvature condition using a Gardner transformation. Employing twoof those charges in the definition of a Hamiltonian allows to view theHirota equationsas an integrablePT-symmetric extension of the nonlinear Schrödinger equation. Weconstruct new degenerate multi-soliton solutions from Hirota’sdirect method as well asDarboux-Crum transformations based on Jordan states. We study the properties of thesesolutions, computing their asymptotic time-dependent displacements and also show thattheir scattering process has a distinct characteristic behaviour different from the nonde-generate counterparts allowing only for interactions of absorb-emit type.

Publication Type: Article
Additional Information: © 2019 Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Hirota equation, PT-symmetry, Darboux-Crum-Crum transformation, Multi-soliton solutions
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering
URI: http://openaccess.city.ac.uk/id/eprint/22289
[img] Text - Accepted Version
This document is not freely accessible until 21 May 2020 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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