中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40304-040304.doi: 10.1088/1674-1056/19/4/040304
吴勇旗
收稿日期:
2009-08-26
修回日期:
2009-09-15
出版日期:
2010-04-15
发布日期:
2010-04-15
基金资助:
Wu Yong-Qi(吴勇旗)†
Received:
2009-08-26
Revised:
2009-09-15
Online:
2010-04-15
Published:
2010-04-15
Supported by:
摘要: The bilinear form of two nonlinear evolution equations are derived by using Hirota derivative. The B\"{a}cklund transformation based on the Hirota bilinear method for these two equations are presented, respectively. As an application, the explicit solutions including soliton and stationary rational solutions for these two equations are obtained.
中图分类号: (Solitons)
吴勇旗. Bilinear B?cklund transformation and explicit solutions for a nonlinear evolution equation[J]. 中国物理B, 2010, 19(4): 40304-040304.
Wu Yong-Qi(吴勇旗). Bilinear B?cklund transformation and explicit solutions for a nonlinear evolution equation[J]. Chin. Phys. B, 2010, 19(4): 40304-040304.
[1] | Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia, PA: SIAM) |
[2] | Novikov S, Manakov S V, Pitaevskii L P and Zakharov V E 1984 Theory of Solitons, The Inverse Scattering Methods (New York: Consultants Bureau) |
[3] | Newell A C 1985 Solitons in Mathematics and Physics (Philadelphia, PA: SIAM) |
[4] | Belokolos E D, Bobenko A I, Enolskii V Z, Its A R and Matveev V B 1994 Algebro-Geometric Approach to Nonlinear Integrable Equations (Berlin: Springer) |
[5] | Cherednik I 1996 Basic Methods of Soliton Theory (Singapore: World Scientific) |
[6] | Matsuno Y 1984 Bilinear Transformation Method (London: Academic Press, Inc.) |
[7] | Hirota R 2004 The Direct Method in Soliton Theory (Cambridge: Cambridge University Press) |
[8] | Konopelchenko B, Sidorenko J and Strampp W 1991 Phys. Lett. A 157 17 |
[9] | Chen Y and Li Y S 1991 Phys. Lett. A 157 22 |
[10] | Cao C W, Wu Y T and Geng X G 1999 J. Math. Phys. 40 3948 |
[11] | Cao C W, Geng X G and Wu Y T 1999 J. Phys. A 32 8059 |
[12] | Geng X G, Wu Y T and Cao C W 1999 J. Phys. A 32 3733 |
[13] | Zhou R G 1997 J. Math. Phys. 38 2535 |
[14] | Wang M L 1995 Phys. Lett. A 199 169 |
[15] | Lei Y 1999 Phys. Lett. A 260 55 |
[16] | Fan E G and Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese) |
[17] | Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) |
[18] | Parkes E J and Duffy B R 1997 Phys. Lett. A 229 217 |
[19] | Zhang G X, Li Z B and Duan Y S 2000 Sci. Chin. A 30 1103 (in Chinese) |
[20] | Fan E G 2000 Phys. Lett. A 277 212 |
[21] | Shi Y R, Lü K P, Duan W S and Zhao J B 2001 Acta Phys. Sin. 50 2074 (in Chinese) |
[22] | Guo G P and Zhang J F 2002 Acta Phys. Sin. 51 1159 (in Chinese) |
[23] | Liu S K, Fu Z T, Liu S D and Zhao Q 2001 Phys. Lett. A 289 69 |
[24] | Fu Z T, Liu S K, Liu S D and Zhao Q 2001 Phys. Lett. A 290 72 |
[25] | Bogoyavlenskii O I 1990 Russ. Math. Surveys 45 1 |
[26] | Radha R and Lakshmanan M 1995 Phys. Lett. A 197 7 |
[27] | Ikeda T and Takasaki K 2001 Int. Math. Res. Notices 7 329 |
[28] | Lou S Y and Ruan H Y 2001 J. Phys. A 34 305 |
[29] | Zhang J F and Meng J P 2004 Phys. Lett. A 321 173 |
[30] | Xie Z and Zhang H Q 2005 Commun. Theor. Phys. 43 401 |
[31] | Wang D S and Li H B 2007 Appl. Math. Comput. 188 762 |
[32] | Huang W H, Liu Y L and Zhang J F 2008 Commun. Theor. Phys. 49 268 |
[33] | Chen L X and Zhang J X 2008 Appl. Math. Comput. 198 184 |
[34] | Fan E G and Hon Y C 2008 Phys. Rev. E 78 036607 |
[35] | Swnatorski A and Infeld E 1996 Phys. Rev. Lett. 77 2855 |
[36] | Chen Y, Yan Z Y and Zhang H Q 2003 Phys. Lett. A 307 107 |
[37] | El-Sayed S M and Kaya D 2004 Appl. Math. Comput. 157 523 |
[38] | Hu J Q 2005 Chaos, Solitons and Fractals 23 391 |
[39] | Liu N and Liu X Q 2008 Chin. Phys. Lett. 25 3527 |
[1] | Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems[J]. 中国物理B, 2023, 32(3): 30506-030506. |
[2] | Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505. |
[3] | Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Modulational instability of a resonantly polariton condensate in discrete lattices[J]. 中国物理B, 2023, 32(3): 30502-030502. |
[4] | Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. 中国物理B, 2023, 32(2): 20201-020201. |
[5] | Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. 中国物理B, 2023, 32(2): 20504-020504. |
[6] | D Chevizovich, S Zdravković, A V Chizhov, and Z Ivić. Charge self-trapping in two strand biomolecules: Adiabatic polaron approach[J]. 中国物理B, 2023, 32(1): 10506-010506. |
[7] | Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505. |
[8] | Jing Wang(王静), Hua Wu(吴华), and Da-Jun Zhang(张大军). Reciprocal transformations of the space-time shifted nonlocal short pulse equations[J]. 中国物理B, 2022, 31(12): 120201-120201. |
[9] | Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation[J]. 中国物理B, 2022, 31(11): 110201-110201. |
[10] | Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502. |
[11] | Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯). Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters[J]. 中国物理B, 2022, 31(8): 80202-080202. |
[12] | Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Oscillation properties of matter-wave bright solitons in harmonic potentials[J]. 中国物理B, 2022, 31(8): 80506-080506. |
[13] | Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation[J]. 中国物理B, 2022, 31(7): 70201-070201. |
[14] | Ahmet Bekir and Emad H M Zahran. Nonlinear dynamical wave structures of Zoomeron equation for population models[J]. 中国物理B, 2022, 31(6): 60401-060401. |
[15] | Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201. |
|