Caudrelier, V orcid.org/0000-0003-0129-6758, Gkogkou, A and Prinari, B (Cover date: July 2023) Soliton interactions and Yang–Baxter maps for the complex coupled short-pulse equation. Studies in Applied Mathematics, 151 (1). pp. 285-351. ISSN 0022-2526
Abstract
The complex coupled short-pulse equation (ccSPE) describes the propagation of ultrashort optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton solutions: fundamental solitons, fundamental breathers, composite breathers (generic or nongeneric), as well as so-called self-symmetric composite solitons. In this work, we use the dressing method and the Darboux matrices corresponding to the various types of solitons to investigate soliton interactions in the focusing ccSPE. The study combines refactorization problems on generators of certain rational loop groups, and long-time asymptotics of these generators, as well as the main refactorization theorem for the dressing factors that leads to the Yang–Baxter property for the refactorization map and the vector soliton interactions. Among the results obtained in this paper, we derive explicit formulas for the polarization shift of fundamental solitons that are the analog of the well-known formulas for the interaction of vector solitons in the Manakov system. Our study also reveals that upon interacting with a fundamental breather, a fundamental soliton becomes a fundamental breather and, conversely, that the interaction of two fundamental breathers generically yields two fundamental breathers with a polarization shifts, but may also result into a fundamental soliton and a fundamental breather. Explicit formulas for the coefficients that characterize the fundamental breathers, as well as for their polarization vectors are obtained. The interactions of other types of solitons are also derived and discussed in detail and illustrated with plots. New Yang–Baxter maps are obtained in the process.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Wiley Periodicals LLC. This is the peer reviewed version of the following article: Caudrelier, V, Gkogkou, A, Prinari, B. Soliton interactions and Yang–Baxter maps for the complex coupled short-pulse equation. Stud Appl Math. 2023; 151: 285– 351, which has been published in final form at https://doi.org/10.1111/sapm.12580. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. |
Keywords: | complex coupled short-pulse equation, solitons, Yang–Baxter maps |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 13 Apr 2023 09:59 |
Last Modified: | 05 May 2024 00:13 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1111/sapm.12580 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198151 |