(2+1)维Korteweg-de Vries方程的复合波解及局域激发

张文玲; 马松华; 陈晶晶

doi:10.7498/aps.63.080506

摘要

借助 Maple 符号计算软件，利用 Riccati 方程（ξ’=a0+a1ξ+a2ξ2）展开法和变量分离法，得到了（2+1）维 Korteweg-de Vries 方程（KdV）包含 q=C1x+C2y+C3t+R（x，y，t）的复合波解. 根据得到的孤立波解，构造出 KdV 方程新颖的复合波裂变和复合波湮灭等局域激发结构.

关键词:

With the help of the symbolic computation system Maple and Riccati equation (ξ’=a0+a1ξ+a2ξ2) expansion method and a variable separation method, some complex wave solutions with q=C1x+C2y+C3t+R(x,y,t) of the (2+1)-dimensional Korteweg-de Vries system is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations such as complex wave fusion and complex wave annihilation are investigated.

Keywords:

作者及机构信息

1.
丽水学院理学院, 丽水 323000

基金项目: 国家自然科学基金（批准号：11375079）、浙江省自然科学基金（批准号：Y6100257，Y6110140）和浙江省教育厅科研基金（批准号：Y201120994）资助的课题.

Authors and contacts

1.
College of Science, Lishui University, Lishui 323000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11375079), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6100257, Y6110140), and the Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant No. Y201120994)

参考文献

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[2]	Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601
[3]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[4]	Hietarinta J 1990 Phys. Lett. A 149 113
[5]	Fokas A S 1998 Phys. Lett. A 132 432
[6]	Zhang D J 2003 Chaos Soliton. Fract. 18 31
[7]	Zhang D J 2005 Chaos Soliton. Fract. 23 1333
[8]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[9]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[10]	Dai C Q, Zhou G Q 2007 Chin. Phys. B 16 1201
[11]	Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12]	Dai C Q, Zhu H P 2013 J. Opt. Soc. Am. B 30 3291
[13]	Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 物理学报 58 2121]
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[16]	Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2009 物理学报 58 7397]
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[18]	Zhang J F 2002 Commun. Theor. Phys. 37 277
[19]	Lou S Y 1996 Commun. Theor. 26 487
[20]	Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[21]	Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 物理学报 54 2990]
[22]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [方建平, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]
[23]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华, 强继业, 方建平 2007 物理学报 56 620]
[24]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 物理学报 55 5611]
[25]	Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[26]	Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[27]	Ma S H, Fang J P, Zheng C L 2009 Chaos Soliton. Fract. 40 210
[28]	Ma S H, Fang J P, Ren Q B 2010 Acta Phys. Sin. 59 4420 (in Chinese) [马松华, 方建平, 任清褒 2010 物理学报 59 4420]
[29]	Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch. 68a 350
[30]	Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[31]	Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[32]	Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[33]	Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. (Beijing, China) 44 209
[34]	Calogero F 1975 Lett. Nouvo Cimento. 14 443
[35]	Lou S Y, Ruan H Y 2001 J. Phys. A 34 305

施引文献

[1]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2]	Tang X Y, Lou S Y, Zhang Y 2002 Phys. Rev. E 66 046601
[3]	Lou S Y 1998 Phys. Rev. Lett. 80 5027
[4]	Hietarinta J 1990 Phys. Lett. A 149 113
[5]	Fokas A S 1998 Phys. Lett. A 132 432
[6]	Zhang D J 2003 Chaos Soliton. Fract. 18 31
[7]	Zhang D J 2005 Chaos Soliton. Fract. 23 1333
[8]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[9]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[10]	Dai C Q, Zhou G Q 2007 Chin. Phys. B 16 1201
[11]	Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12]	Dai C Q, Zhu H P 2013 J. Opt. Soc. Am. B 30 3291
[13]	Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 2121 (in Chinese) [套格图桑, 斯仁道尔吉 2009 物理学报 58 2121]
[14]	Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 5887 (in Chinese) [套格图桑, 斯仁道尔吉 2009 物理学报 58 5887]
[15]	Ma Y L, Li B Q, Sun J Z 2009 Acta Phys. Sin. 58 7402 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 物理学报 58 7402]
[16]	Mo J Q, Zhang W J, Chen X F 2009 Acta Phys. Sin. 58 7397 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2009 物理学报 58 7397]
[17]	Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[18]	Zhang J F 2002 Commun. Theor. Phys. 37 277
[19]	Lou S Y 1996 Commun. Theor. 26 487
[20]	Lou S Y, Tang X Y, Li J 2001 Eue. Phys. J. B 22 473
[21]	Fang J P, Zheng C L, Zhu J M 2005 Acta Phys. Sin. 54 2990 (in Chinese) [方建平, 郑春龙, 朱加民 2005 物理学报 54 2990]
[22]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [方建平, 吴小红, 方建平, 郑春龙 2008 物理学报 57 11]
[23]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华, 强继业, 方建平 2007 物理学报 56 620]
[24]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 物理学报 55 5611]
[25]	Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[26]	Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[27]	Ma S H, Fang J P, Zheng C L 2009 Chaos Soliton. Fract. 40 210
[28]	Ma S H, Fang J P, Ren Q B 2010 Acta Phys. Sin. 59 4420 (in Chinese) [马松华, 方建平, 任清褒 2010 物理学报 59 4420]
[29]	Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch. 68a 350
[30]	Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[31]	Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[32]	Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[33]	Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. (Beijing, China) 44 209
[34]	Calogero F 1975 Lett. Nouvo Cimento. 14 443
[35]	Lou S Y, Ruan H Y 2001 J. Phys. A 34 305

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