S. B. SHAN ET AL.
Copyright © 2013 SciRes. OJAppS
101
(a)
(b)
Figure 4. The third order rogue wave solution |Qr3|2 of the
Kundu-DNLS equation w ith (a) a = –2, c = 1, S0 = 0, S1 =
500, S2 = 0; (b) a = –2, c = 1, S0 = 0, S1 = 0, S2 = 1000.
We can split the third order rogue wave solution into
triangle structure. A particular structure is displayed in
Figure 4(a). The third-order rogue wave is seen to pos-
sess a regular triangle spatial symmetry structure.
What's more, we also can split the third order rogue
wave solution into pentagon structure. A particular struc-
ture is displayed in Figure 4(b). The third-order rogue
wave exhibits a regular pentagon spatial symmetry
structure.
4. Conclusions
In this paper, we construct the Darboux transformation
for the Kundu-DNLS equation. This Darboux transfor-
mation, in particular, allows us to calculate higher order
rogue wave solutions in a unified way. In this way, we
can derive the higher order rogue wave solutions for
Kundu-DNLS equation by making use of the Darboux
transformation. Particularly, these rogue wave solutions
possess several free parameters. With the help of these
parameters, these rogue waves constitute some patterns,
such as fundamental pattern, triangular pattern, circular
pattern.
5. Acknowledgements
This work is supported by the NSF of China under Grant
No.11271210 and K. C. Wong Magna Fund in Ningbo
University. Jingsong He is also supported by Natural
Science Foundation of Ningbo under Grant No.
2011A610179. Chuanzhong Li is supported by the Na-
tional Natural Science Foundation of China under Grant
No.11201251, the Natural Science Foundation of Zheji-
ang Province under Grant No. LY12A01007. We thank
Prof. Yishen Li (USTC, Hefei, China) for his long time
support and useful suggestions.
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