Fu, W and Nijhoff, F (2022) On A Coupled Kadomtsev–Petviashvili System Associated With an Elliptic Curve. Studies in Applied Mathematics, 149 (4). pp. 1086-1122. ISSN 0022-2526
Abstract
The coupled Kadomtsev–Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo, and Miwa [J. Phys. Soc. Jpn., 52:766–771, 1983], is reinvestigated within the direct linearization framework, which provides us with more insights into the integrability of this elliptic model from the perspective of a general linear integral equation. As a result, we successfully construct for the elliptic coupled Kadomtsev–Petviashvili system not only a Lax pair composed of differential operators in 2 × 2 matrix form but also multisoliton solutions with phases parametrized by points on the elliptic curve. Dimensional reductions based on the direct linearization, to the elliptic coupled Korteweg–de Vries and Boussinesq systems, are also discussed. In addition, a novel class of solutions is obtained for the
D∞-type Kadomtsev–Petviashvili equation with nonzero constant background as a by-product.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Wiley Periodicals LLC. This is the peer reviewed version of the following article: Fu, W, Nijhoff, FW. On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve. Stud Appl Math. 2022; 149: 1086–1122, which has been published in final form at https://doi.org/10.1111/sapm.12529. 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: | DKP; direct linearization; dimensional reduction; elliptic coupled KP; Lax pair; τ-function; nonzero constant background; solitons |
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: | 03 Aug 2022 14:38 |
Last Modified: | 16 Aug 2023 00:13 |
Status: | Published |
Publisher: | Wiley |
Identification Number: | 10.1111/sapm.12529 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:189675 |