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
Received:
23
March
2024
Accepted:
14
July
2024
Published online:
25
July
2024
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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