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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