Rogue wave solutions of the nonlinear Schr?dinger equation with variable coefficients

详细信息    查看全文

• 作者：CHANGFU LIU ; YAN YAN LI ; MEIPING GAO ; ZEPING WANG ; ZHENGDE DAI ; CHUANJIAN WANG
• 关键词：Nonlinear Schr?dinger equation ; exp ; function method ; breather soliton ; rogue wave. ; 02.30.Jr ; 05.45.Yv ; 03.65.Ge
• 刊名：Pramana
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：85
• 期：6
• 页码：1063-1072
• 全文大小：1,510 KB
• 参考文献：[1]R Y Hao, A T Ju, F Q Wang and G S Zhou, Opt. Commun. 281, 5898 (2008)
  [2]J F Zhang, C Q Dai, Q Yang and J M Zhu, Opt. Commun. 252, 408 (2005)
  [3]J F Zhang, M Z Jin, J D He, J H Lou and C Q Dai, Chin. Phys. B 22, 054208 (2013)
  [4]D H Peregrine, J. Aust. Math. Soc. Ser. B: Appl. Math. 25, 16 (1983)
  [5]P Müller, C Garrett and A Osborne, Oceanography 18, 66 (2005)
  [6]F Fedele, Physica D 237, 2127 (2008)
  [7]A Chabchoub, N P Hoffmann and N Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)
  [8]W M Moslem, P K Shukla and B Eliasson, Europhys. Lett. 96, 25002 (2011)
  [9]D R Solli, C Ropers, P Koonath and B Jalali, Nature 450, 1054 (2007)
  [10]A Zaviyalov, O Egorov, R Iliew and F Lederer, Phys. Rev. A 85, 013828 (2012)
  [11]C Bonatto, M Feyereisen, S Barland, M Giudici, C Masoller, J R Rios Leite and J R Tredicce, Phys. Rev. Lett. 107, 053901 (2011)
  [12]S Vergeles and S K Turitsyn, Phys. Rev. A 83, 061801(R) (2011)
  [13]J S He, S W Xu and K Porsezian, Phys. Rev. E 86, 066603 (2012)
  [14]C Z Li, C Liu and Z Y Yang, Commun. Nonlinear Sci. Numer. Simul. 20, 9 (2015)
  [15]V B Efimov, A N Ganshin, G V Kolmakov, P V E McClintock and L P Mezhov-Deglin, Eur. Phys. J. Spec. Top. 185, 181 (2010)
  [16]Yu V Bludov, V V Konotop and N Akhmediev, Phys. Rev. A 80, 033610 (2009)
  [17]B L Guo and L M Ling, Chin. Phys. Lett. 28, 110202 (2011)
  [18]M Shats, H Punzmann and H Xia, Phys. Rev. Lett. 104, 104503 (2010)
  [19]A Ankiewicz, Y Wang, S Wabnitz and N Akhmediev, Phys. Rev. E 89, 012907 (2014)
  [20]L H Wang, K Porsezian and J S He, Phys. Rev. E 87, 053202 (2013)
  [21]A Chabchoub and M Fink, Phys. Rev. Lett. 112, 124101 (2014)
  [22]L M Ling, B L Guo and L C Zhao, Phys. Rev. E 89, 041201 (2014)
  [23]J S He, H R Zhang, L H Wang, K Porsezian and A S Fokas, Phys. Rev. E 87, 052914 (2013)
  [24]W P Zhong, M R Beli? and T W Huang, Phys. Rev. E 87, 065201 (2013)
  [25]Z Y Ma and S H Ma, Chin. Phys. B 21, 030507 (2012)
  [26]Z Y Yan, Commun. Theor. Phys. (Beijing, China) 54, 947 (2010)
  [27]Y Y Wang, J S He and Y S Li, Commun. Theor. Phys. (Beijing, China) 56, 995 (2011)
  [28]X C Wang, J S He and Y S Li, Commun. Theor. Phys. (Beijing, China) 56, 631 (2011)
  [29]N Akhmediev, A Ankiewicz and J M Soto-Crespo, Phys. Rev. E 80,026601 (2009)
  [30]Y C Ma, Stud. Appl. Math. 60, 43 (1979)
  [31]K L Henderson, D H Peregrine and J W Dold, Wave Motion 29, 341 (1999)
  [32]N Akhmediev, A Ankiewicz and M Taki, Phys. Lett. A 373, 675 (2009)
  [33]N Akhmediev, J M Soto-Crespo and A Ankiewicz, Phys. Lett. A 373, 2137 (2009)
  [34]J H He and X H Wu, Chaos, Solitons and Fractals 30, 700 (2006)
  [35]C J Wang and Z D Dai, Adv. Diff. Equat. 1, 87 (2014)
  [36]Z Y Yan, V V Konotop and N Akhmediev, Phys. Rev. E 82, 036610 (2010)
  [37]J S He, E G Charalampidis, P G Kevrekidis and D J Frantzeskakis, Phys. Lett. A 378, 577 (2014)
  [38]Z Y Yan, Phys. Lett. A 374, 672 (2010)
  
• 作者单位：CHANGFU LIU (1)
  YAN YAN LI (1)
  MEIPING GAO (1)
  ZEPING WANG (1)
  ZHENGDE DAI (2)
  CHUANJIAN WANG (3)
  
  1. School of Mathematics, Wenshan University, Wenshan, 663000, People’s Republic of China
  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, People’s Republic of China
  3. School of Science, Kunming University of Science and Technology, Kunming, 650031, People’s Republic of China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Astronomy
  Astrophysics
  
• 出版者：Springer India
• ISSN：0973-7111

文摘

In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schr?dinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schr?dinger equation are also obtained. Two free functions of time t and several arbitrary parameters are involved to generate a large number of wave structures. Keywords Nonlinear Schr?dinger equation exp-function method breather soliton rogue wave.