1. Characteristics of rogue waves on a periodic background for the Hirota equation.
- Author
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Peng, Wei-Qi, Tian, Shou-Fu, Wang, Xiu-Bin, and Zhang, Tian-Tian
- Subjects
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ROGUE waves , *ELLIPTIC functions , *EQUATIONS , *WAVE equation , *DARBOUX transformations , *EIGENFUNCTIONS , *LAX pair , *COMPUTER simulation - Abstract
We consider the rogue dn-periodic waves (the rogue wave solutions on the dn-periodic waves background) for the Hirota equation by using Darboux transformation. We take Jacobian elliptic function dn as a seed solution, which is modulationally unstable as regards long wave perturbations. Through nonlinearization of the Lax pair for Hirota equation, the corresponding periodic eigenfunctions are successfully obtained. Based on these periodic eigenfunctions, we further construct the solutions of the Lax pair equations with dn-periodic wave seed solutions. In addition, numerical simulations are presented to reveal the phenomena of these solutions under different parameters choices. • We consider the rogue periodic waves for the Hirota equation. • Jacobian elliptic function solution is considered for regarding long wave perturbations. • We obtain the corresponding periodic eigenfunctions. • We further construct the solutions of the Lax pair equations with periodic wave seed solutions. • Numerical simulations are presented to reveal the phenomena of these solutions under different parameters choices. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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