Soliton Solutions to the Coupled Gerdjikov–Ivanov Equation with Rogue-Wave-Like Phenomena
Jian-Bing Zhang1** , Ying-Yin Gongye1 , Shou-Ting Chen2
1 School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 2211162 School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou 221008
Abstract ：Bilinear forms of the coupled Gerdjikov–Ivanov equation are derived. The $N$-soliton solutions to the equation are obtained by Hirota's method. It is interesting that the two-soliton solutions can generate the rogue-wave-like phenomena by selecting special parameters. The equation can be reduced to the Gerdjikov–Ivanov equation as well as its bilinear forms and its solutions.
收稿日期: 2017-04-18
出版日期: 2017-08-15
[1] Johnson R S 1977 Proc. R. Soc. Lond. Ser. A 357 131 [2] Kodama Y 1985 J. Stat. Phys. 39 597 [3] Clarkson P A and Tuszynski J A 1990 J. Phys. A 23 4269 [4] Kaup D J and Newell A C 1978 J. Math. Phys. 19 798 [5] Chen H H, Lee Y C and Liu C S 1979 Phys. Scr. 20 490 [6] Kakei S, Sasa N and Satsuma J 1995 J. Phys. Soc. Jpn. 64 1519 [7] Gerdjikov V S and Ivanov M I 1983 Bull. J. Phys. 10 130 [8] Kundu A 1987 Physica D 25 399 [9] Clarkson P A and Cosgrove C M 1987 J. Phys. A 20 2003 [10] Zhang J B, Chen S T and Li Q 2013 Phys. Scr. 88 065006 [11] Zhang J B, Zhang D J and Shen Q 2011 Appl. Math. Comput. 218 4494 [12] Zhang J B, Zhang D J and Chen D Y 2010 Commun. Theor. Phys. 53 211 [13] Fan E G 2000 J. Math. Phys. 41 7769 [14] Yu J, He J S and Han J W 2012 J. Math. Phys. 53 033708 [15] Fan E G 2000 J. Phys. A 33 6925 [16] Fan E G 2001 Commun. Theor. Phys. 35 651 [17] Liu Y K and Li B 2017 Chin. Phys. Lett. 34 010202 [18] Qian C, Rao J G, Liu Y B and He J S 2016 Chin. Phys. Lett. 33 110201 [19] Xu S W and He J S 2012 J. Math. Phys. 53 063507 [20] Guo L et al 2014 Phys. Scr. 89 035501 [21] Dai H H and Fan E G 2004 Chaos Solitons & Fractals 22 93 [22] Hou Y, Fan E G and Zhao P 2013 J. Math. Phys. 54 073505 [23] Takahashi M and Konno K 1989 J. Phys. Soc. Jpn. 58 3505 [24] Zhou J, Zhang D J and Zhao S L 2009 Phys. Lett. A 373 3248
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2017, Vol. 34 
