Characteristics of rogue waves on a periodic background for the Hirota equation |
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| Institution: | 1. Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China;2. Research Center for Ecological Engineering and Nonlinear Science, North China Electric Power University, Beijing 102206, PR China;3. Institute of electrical and electronic engineering, North China Electric Power University, Beijing 102206, PR China;4. School of Information, Beijing Wuzi University, Beijing 101149, PR China |
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| 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. |
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| Keywords: | Hirota equation Darboux transformation Rogue dn-periodic waves Jacobian elliptic function Periodic eigenfunctions |
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