Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation
Cen, J. & 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 Science & Technology |
| SWORD Depositor: |
Available under License Creative Commons Attribution Non-commercial No Derivatives.
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