Please wait a minute...
Chin. Phys. B, 2016, Vol. 25(4): 040202    DOI: 10.1088/1674-1056/25/4/040202
GENERAL Prev   Next  

(2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect

Jin-Yuan Li(李近元)1,2,3, Nian-Qiao Fang(方念乔)1, Ji Zhang(张吉)2,3, Yu-Long Xue(薛玉龙)4, Xue-Mu Wang(王雪木)4, Xiao-Bo Yuan(袁晓博)1
1 School of Ocean Sciences, China University of Geosciences (Beijing), Beijing 100083, China;
2 Marine Geology and Hydrology Research Laboratory, Guodian New Energy Technology Research Institute, Beijing 102209, China;
3 Zhong Neng Power-Tech Development Company Limited, Beijing 100034, China;
4 Marine Geological Institute of Hainan Province, Haikou 570206, China
Abstract  In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.
Keywords:  (2+1)-dimensional dissipation nonlinear Schrödinger equation      envelope Rossby solitary waves      chirp effect      two-soliton solutions  
Received:  06 September 2015      Revised:  25 November 2015      Published:  05 April 2016
PACS:  02.30.Jr (Partial differential equations)  
  47.35.Fg (Solitary waves)  
  92.10.Hm (Ocean waves and oscillations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 41406018).
Corresponding Authors:  Jin-Yuan Li     E-mail:  lijinyuan198007@sina.com

Cite this article: 

Jin-Yuan Li(李近元), Nian-Qiao Fang(方念乔), Ji Zhang(张吉), Yu-Long Xue(薛玉龙), Xue-Mu Wang(王雪木), Xiao-Bo Yuan(袁晓博) (2+1)-dimensional dissipation nonlinear Schrödinger equation for envelope Rossby solitary waves and chirp effect 2016 Chin. Phys. B 25 040202

[1] Long R R, Andrushkiw R I and Huang X H 1964 J. Atmos. Sci. 21 197
[2] Benney D J 1966 J. Math. Phys. 45 52
[3] Redekopp L G 1977 J. Fluid. Meth. 82 725
[4] Boyd J P 1980 J. Phys. Ocean. 10 1699
[5] Grimshaw R H J 1981 Stud. Appl. Math. 65 159
[6] Yang H W, Yin B S, Yang D Z and Xu Z H 2011 Chin. Phys. B 20 120203
[7] Wadati M 1973 J. Phys. Soc. Jpn. 34 1289
[8] Song J and Yang L G 2009 Chin. Phys. B 18 2873
[9] Yang H W, Yin B S and Shi Y L 2012 Nonlinear Dyn. 70 1389
[10] Ono H 1981 J. Phys. Soc. Japan 50 2757
[11] Yang H W, Yin B S, Dong H H and Shi Y L 2012 Commun. Theor. Phys. 58 425
[12] Kubota T, Ko D R S and Dobbs L D 1978 J. Hydro. 12 157
[13] Yang H W, Yin B S, Zhong B and Dong H H 2013 Adv. Mech. Eng. 2013 289269
[14] Benney D J 1979 Stud. Appl. Math. 60 1
[15] Yamagata T 1980 Jpn. J. Meteor. Soc. 58 160
[16] Luo D H 2005 J Atmos. Sci. 62 5
[17] Luo D H 2001 Wave Motion 33 339
[18] Song S Y, Wang J, Wang J B, Song S S and Meng J M 2010 Acta Phys. Sin. 59 6339 (in Chinese)
[19] Han L B, Deng X J and Yan Z Z 2009 Chin. Phys. B 18 3169
[20] Zhao Q and Liu S K 2006 Chin. J. Geophys. 49 965
[21] Chen J C, Li B and Chen Yong 2013 Chin. Phys. B 22 110306
[22] Hu X R and Chen Y 2015 Chin. Phys. B 24 030201
[23] Matveev V B and Salle M A 1991 Darboux Transformation and Solitons (Berlin: Springer)
[24] Dong H H and Zhang Y F 2015 Commun. Theor. Phys. 63 401
[1] Observation of the near transform-limited high-resolution tunable far-ultraviolet light
Zheng Huai-Bin, Zhang Yan-Peng, Nie Zhi-Qiang, Li Chang-Biao, Song Jian-Ping, Li Chuang-She, Lu Ke-Qing. Chin. Phys. B, 2009, 18(7): 2729-2733.
No Suggested Reading articles found!