Geodesic
Rogue-wave solutions of the~Zakharov equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 434-454

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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.
Mots-clés : Zakharov equation, rogue wave.
Keywords: bilinear transformation method 
@article{TMF_2017_193_3_a4,
     author = {Jiguang Rao and Lihong Wang and Wei Liu and Jingsong He},
     title = {Rogue-wave solutions of {the~Zakharov} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {434--454},
     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a4/}
}
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Jiguang Rao; Lihong Wang; Wei Liu; Jingsong He. Rogue-wave solutions of the~Zakharov equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 3, pp. 434-454. http://geodesic.mathdoc.fr/item/TMF_2017_193_3_a4/