Chin. Phys. Lett.  2014, Vol. 31 Issue (06): 060201    DOI: 10.1088/0256-307X/31/6/060201
GENERAL |
Rogue Wave Solutions for the Heisenberg Ferromagnet Equations
ZHANG Yan, NIE Xian-Jia, ZHA Qi-Lao**
College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022
Cite this article:   
ZHANG Yan, NIE Xian-Jia, ZHA Qi-Lao 2014 Chin. Phys. Lett. 31 060201
Download: PDF(888KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract Darboux transformation of the Heisenberg ferromagnet equation is constructed by the Darboux matrix method. In application, the rogue wave solutions of the Heisenberg ferromagnet equation are obtained. In particular, rogue waves are discussed and illustrated.
Published: 26 May 2014
PACS:  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/31/6/060201       OR      https://cpl.iphy.ac.cn/Y2014/V31/I06/060201
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
ZHANG Yan
NIE Xian-Jia
ZHA Qi-Lao
[1] Müller P, Garrett C and Osborne A 2005 Oceanography 18 66
[2] Drape L 1965 Mar. Obs. 35 193
[3] Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 373 675
[4] Akhmediev N, Dudly J M, Solli D R and Turitsym S K 2013 J. Opt. 15 060201
[5] Akhmediev N and Pelinovsky E 2010 Eur. Phys. J.: Spec. Top. 185 1
[6] Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054
[7] Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202
[8] He J S, Wang Y Y and Li L J 2012 Chin. Phys. Lett. 29 060509
[9] Liu C, Yang Z Y, Zhao L C, Yang W L and Yue R H 2013 Chin. Phys. Lett. 30 040304
[10] Cai W J, Wang Y S and Song Z 2014 Chin. Phys. Lett. 31 040201
[11] Bluclov Yu V, Konotop V V and Akhmediev N 2009 Phys. Rev. A 80 033610
[12] Kharif C, Pelinovsky E and Slunyaev A 2009 Rogue Waves in the Ocean (Berlin: Springer)
[13] Kharif C and Pelinovsky E 2003 Eur. J. Mech. B 22 603
[14] Peregrine D H 1983 J. Austral. Math. Soc. Ser. B: Appl. Math. 25 16
[15] Akhmediev N, Ankiewicz A and Soto-Grespo J M 2009 Phys. Rev. E 80 026601
[16] Ankiewicz A, Kedziora D J and Akhmediev N 2011 Phys. Lett. A 375 2782
[17] Kedziora D J, Ankiewicz A and Akhmediev N 2011 Phys. Rev. E 84 056611
[18] Guo B L, Ling L M and Liu Q P 2012 Phys. Rev. E 85 026607
[19] He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2013 Phys. Rev. E 87 052914
[20] Zhai B G, Zhang W G, Wang X L and Zhang H Q 2013 Nonlinear Anal.: Real World Appl. 14 14
[21] Tao Y S, He J S and Porsezian K 2013 Chin. Phys. B 22 074210
[22] Wang H and Lin B 2011 Chin. Phys. B 20 040203
[23] Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press)
[24] Li Y S 1990 Soliton and Integrable System (Shanghai: Shanghai Scientific and Technological Education Publishing House)
[25] Rogers C and Schief W K 2002 B?lund and Darboux Transformations Geometry and Modern Applications in Soliton Theory (Cambridge: Cambridge University Press)
[26] Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
[27] Gu C H, Hu H S and Zhou Z X 2005 Darboux Transformations in Integrable Systems: Theory and Their Applications to Geometry (Dordrecht: Springer)
[28] Lakshmanan M 1977 Phys. Lett. A 61 53
[29] Takhtajan L A 1977 Phys. Lett. A 64 235
[30] Lou S Y and Li Y S 2006 Chin. Phys. Lett. 23 2633
[31] Zhaqilao 2012 Phys. Lett. A 376 3121
[32] Zhaqilao 2013 Phys. Scr. 87 065401
Related articles from Frontiers Journals
[1] S. Y. Lou, Man Jia, and Xia-Zhi Hao. Higher Dimensional Camassa–Holm Equations[J]. Chin. Phys. Lett., 2023, 40(2): 060201
[2] Wen-Xiu Ma. Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions[J]. Chin. Phys. Lett., 2022, 39(10): 060201
[3] Chong Liu, Shao-Chun Chen, Xiankun Yao, and Nail Akhmediev. Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations[J]. Chin. Phys. Lett., 2022, 39(9): 060201
[4] Xiao-Man Zhang, Yan-Hong Qin, Li-Ming Ling, and Li-Chen Zhao. Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation[J]. Chin. Phys. Lett., 2021, 38(9): 060201
[5] Kai-Hua Yin, Xue-Ping Cheng, and Ji Lin. Soliton Molecule and Breather-Soliton Molecule Structures for a General Sixth-Order Nonlinear Equation[J]. Chin. Phys. Lett., 2021, 38(8): 060201
[6] Yusong Cao and Junpeng Cao. Exact Solution of a Non-Hermitian Generalized Rabi Model[J]. Chin. Phys. Lett., 2021, 38(8): 060201
[7] Zequn Qi , Zhao Zhang , and Biao Li. Space-Curved Resonant Line Solitons in a Generalized $(2+1)$-Dimensional Fifth-Order KdV System[J]. Chin. Phys. Lett., 2021, 38(6): 060201
[8] Wei Wang, Ruoxia Yao, and Senyue Lou. Abundant Traveling Wave Structures of (1+1)-Dimensional Sawada–Kotera Equation: Few Cycle Solitons and Soliton Molecules[J]. Chin. Phys. Lett., 2020, 37(10): 060201
[9] Li-Chen Zhao, Yan-Hong Qin, Wen-Long Wang, Zhan-Ying Yang. A Direct Derivation of the Dark Soliton Excitation Energy[J]. Chin. Phys. Lett., 2020, 37(5): 060201
[10] Danda Zhang, Da-Jun Zhang, Sen-Yue Lou. Lax Pairs of Integrable Systems in Bidifferential Graded Algebras[J]. Chin. Phys. Lett., 2020, 37(4): 060201
[11] Yu-Han Wu, Chong Liu, Zhan-Ying Yang, Wen-Li Yang. Breather Interaction Properties Induced by Self-Steepening and Space-Time Correction[J]. Chin. Phys. Lett., 2020, 37(4): 060201
[12] Bao Wang, Zhao Zhang, Biao Li. Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schr?dinger Equation[J]. Chin. Phys. Lett., 2020, 37(3): 060201
[13] Zhao Zhang, Shu-Xin Yang, Biao Li. Soliton Molecules, Asymmetric Solitons and Hybrid Solutions for (2+1)-Dimensional Fifth-Order KdV Equation[J]. Chin. Phys. Lett., 2019, 36(12): 060201
[14] Zhou-Zheng Kang, Tie-Cheng Xia. Construction of Multi-soliton Solutions of the $N$-Coupled Hirota Equations in an Optical Fiber[J]. Chin. Phys. Lett., 2019, 36(11): 060201
[15] Yong-Shuai Zhang, Jing-Song He. Bound-State Soliton Solutions of the Nonlinear Schr?dinger Equation and Their Asymmetric Decompositions[J]. Chin. Phys. Lett., 2019, 36(3): 060201
Viewed
Full text


Abstract