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Nonlinear Sciences > Pattern Formation and Solitons

arXiv:2102.11523 (nlin)
[Submitted on 23 Feb 2021 (v1), last revised 30 Aug 2021 (this version, v2)]

Title:Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation

Authors:N. Sinthuja, K. Manikandan, M. Senthilvelan
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Abstract:We construct rogue wave solutions of a fifth-order nonlinear Schrödinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave solution on two different periodic wave backgrounds. We analyze the obtained solutions for different values of system parameter and point out certain novel features of our results. We also compute instability growth rate of both $dn$ and $cn$ periodic background waves for the considered system through spectral stability problem. We show that instability growth rate decreases (increases) for $dn$-$(cn)$ periodic waves when we vary the value of the elliptic modulus parameter.
Comments: 26 pages, 7 figures and published in Physics Letters A journal
Subjects: Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:2102.11523 [nlin.PS]
  (or arXiv:2102.11523v2 [nlin.PS] for this version)
  https://doi.org/10.48550/arXiv.2102.11523
Journal reference: Phys. Lett. A 415 (2021) 127640
Related DOI: https://doi.org/10.1016/j.physleta.2021.127640

Submission history

From: K Manikandan [view email]
[v1] Tue, 23 Feb 2021 07:14:23 UTC (505 KB)
[v2] Mon, 30 Aug 2021 06:38:19 UTC (1,853 KB)
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