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TMF, 2017, Volume 193, Number 3, Pages 434–454 (Mi tmf9217)  

This article is cited in 6 scientific papers (total in 6 papers)

Rogue-wave solutions of the Zakharov equation

Jiguang Raoa, Lihong Wangb, Wei Liuc, Jingsong Hea

a Mathematics Department, Faculty of Science, Ningbo University, Ningbo, China
b Faculty of Mechanical Engineering & Mechanics, Ningbo University, Ningbo, China
c School of Mathematical Sciences, University of Science and Technology of China, Hefei, China

Abstract: Using the bilinear transformation method, we derive general rogue-wave solutions of the Zakharov equation. We present these $N$th-order rogue-wave solutions explicitly in terms of $N$th-order determinants whose matrix elements have simple expressions. We show that the fundamental rogue wave is a line rogue wave with a line profile on the plane $(x,y)$ arising from a constant background at $t\ll0$ and then gradually tending to the constant background for $t\gg0$. Higher-order rogue waves arising from a constant background and later disappearing into it describe the interaction of several fundamental line rogue waves. We also consider different structures of higher-order rogue waves. We present differences between rogue waves of the Zakharov equation and of the first type of the Davey–Stewartson equation analytically and graphically.

Keywords: Zakharov equation, bilinear transformation method, rogue wave.

Funding Agency Grant Number
National Natural Science Foundation of China 11671219
K. C. Wong Magna Fund (Ningbo University)
This research is supported by the NSF of China (Grant Nos. 11671219 and 11271210) and the K. C. Wong Magna Fund in Ningbo University.

DOI: https://doi.org/10.4213/tmf9217

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English version:
Theoretical and Mathematical Physics, 2017, 193:3, 1783–1800

Bibliographic databases:

PACS: 02.30.Ik, 05.45.Yv, 42.65.Tg
MSC: 35Q51, 35Q55 37K10, 37K35, 37K40
Received: 27.04.2016
Revised: 24.10.2016

Citation: Jiguang Rao, Lihong Wang, Wei Liu, Jingsong He, “Rogue-wave solutions of the Zakharov equation”, TMF, 193:3 (2017), 434–454; Theoret. and Math. Phys., 193:3 (2017), 1783–1800

Citation in format AMSBIB
\by Jiguang~Rao, Lihong~Wang, Wei~Liu, Jingsong~He
\paper Rogue-wave solutions of the~Zakharov equation
\jour TMF
\yr 2017
\vol 193
\issue 3
\pages 434--454
\jour Theoret. and Math. Phys.
\yr 2017
\vol 193
\issue 3
\pages 1783--1800

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    1. I. Jaradat, M. Alquran, Sh. Momani, A. Biswas, “Dark and singular optical solutions with dual-mode nonlinear Schrödinger's equation and Kerr-law nonlinearity”, Optik, 172 (2018), 822–825  crossref  isi  scopus
    2. C. B. Ward, P. G. Kevrekidis, “Rogue waves as self-similar solutions on a background: a direct calculation”, Rom. J. Phys., 64:7-8 (2019), 112  isi
    3. X. Geng, R. Li, “On a vector modified yajima-oikawa long-wave-short-wave equation”, Mathematics, 7:10 (2019), 958  crossref  isi
    4. R. Li, X. Geng, B. Xue, “A generalization of the Landau-Lifschitz equation: breathers and rogue waves”, J. Nonlinear Math. Phys., 27:2 (2020), 279–294  crossref  mathscinet  isi
    5. W. Liu, Yu. Zhang, “High-order rational solutions and rogue wave for the (2+1)-dimensional nonlinear Schrodinger equation”, Phys. Scr., 95:4 (2020), 045204  crossref  isi
    6. Cao Yu., Hu P.-Ya., Cheng Y., He J., “Deformed Two-Dimensional Rogue Waves in the (2+1)-Dimensional Korteweg-de Vries Equation”, Chin. Phys. B, 30:3 (2021), 030503  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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