https://doi.org/10.1140/epjp/s13360-024-05458-8
Regular Article
Rogue waves on the background of periodic traveling waves in the discrete Hirota equation
School of Mathematics, Southeast University, 210096, Nanjing, China
a
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Received:
23
March
2024
Accepted:
14
July
2024
Published online:
25
July
2024
Abstract
This paper investigates the rogue wave solutions on the periodic background of the discrete Hirota equation. The rogue wave solutions are obtained by using the nonlinearization method with a single eigenvalue and one-fold Darboux transformation. Through nonlinearization method, the periodic squared eigenfunctions and eigenvalues corresponding to traveling periodic waves are successfully obtained. The traveling periodic waves are expressed by the Jacobi dnoidal/cnoidal elliptic functions which are used as the seed solutions. Since the dnoidal/cnoidal waves are modulationally unstable, the rogue waves generated on the periodic background.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
