(2+1)维色散长波方程的新精确解及其复合波激发

林福忠; 马松华

doi:10.7498/aps.63.040508

摘要

利用Riccati方程展开法和变量分离法，得到了（2+1）维色散长波方程的变量分离解. 根据得到的孤波解，构造出该方程新颖的复合波局域结构，研究了复合波随时间的演化.

关键词:

By the Riccati equation expansion method and a variable separation method, a series of variable separation solutions of the (2+1)-dimensional dispersive long wave equation is derived. According to the derived solitary wave solution, we obtain some nove complex wave localized structures and study the time evolutions of complex waves.

Keywords:

Riccati equation expansion method /
(2+1)-dimensional dispersive long wave equation /
variable separation solutions /
complex wave structures

作者及机构信息

林福忠¹,
马松华²

1.
龙岩学院物理系, 龙岩 364012;

2.
丽水学院物理系, 丽水 323000

基金项目: 国家自然科学基金（批准号：11375079）、福建省教育厅科研基金（批准号：JA13305）、浙江省教育厅科研基金（批准号：Y201120994）和浙江省自然科学基金（批准号：Y6100257, Y6110140）资助的课题.

Authors and contacts

Lin Fu-Zhong¹,
Ma Song-Hua²

1.
Department of Physics, Longyan University, Longyan 364012, China;

2.
Department of Physics, Lishui University, Lishui 323000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11375079), the Scientific Research Fund of Fujian Provincial Education Department of China (Grant No. JA13305), the Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant No. Y201120994), and the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6100257, Y6110140).

参考文献

[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]	Ruan H Y, Chen Y X 2001 Acta Phys. Sin. 50 586 (in Chinese) [阮航宇, 陈一新 2001 50 586]
[7]	Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[8]	Lou S Y 2003 J. Phys. A: Math. Gen. 36 3877
[9]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[10]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[11]	Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12]	Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放, 黄文华, 郑春龙 2002 51 2676]
[13]	Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese) [朱加民, 马正义, 郑春龙 2004 53 3248]
[14]	Lou S Y, Tang X Y, Li J 2001 Eur. Phys. J. B 22 473
[15]	Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[16]	Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[17]	Lou S Y 1996 Commun. Theor. 26 487
[18]	Fang J P, Zheng C L, Chen L Q 2004 Commun. Theor. Phys. 42 175
[19]	Boiti M, Leon J J, Manna M, Pempinelli F 1989 Phys. Rev. Lett. A 63 1329
[20]	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 54 2990]
[21]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 57 11]
[22]	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 56 620]
[23]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611]
[24]	Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[25]	Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[26]	Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[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 59 4420]
[29]	Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch 68a 350
[30]	Dai C Q, Zhou G Q 2007 Chin. Phys. 16 1201
[31]	Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[32]	Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[33]	Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. 44 209
[34]	Boiti M, Leon J J, Manna M, Pempinelli F 1986 Inverse Problem 2 271
[35]	Zhang J F 2002 Commun. Theor. Phys. 37 277

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]	Ruan H Y, Chen Y X 2001 Acta Phys. Sin. 50 586 (in Chinese) [阮航宇, 陈一新 2001 50 586]
[7]	Zhang J F, Meng J P 2004 Commun. Theor. Phys. 41 655
[8]	Lou S Y 2003 J. Phys. A: Math. Gen. 36 3877
[9]	Zhang S L, Zhu X N, Wang Y M, Lou S Y 2008 Commun. Theor. Phys. 49 829
[10]	Zhang S L, Lou S Y 2007 Commun. Theor. Phys. 48 385
[11]	Dai C Q, Ni Y Z 2006 Phys. Scripta 74 584
[12]	Zhang J F, Huang W H, Zheng C L 2002 Acta Phys. Sin. 51 2676 (in Chinese) [张解放, 黄文华, 郑春龙 2002 51 2676]
[13]	Zhu J M, Ma Z Y, Zheng C L 2004 Acta Phys. Sin. 53 3248 (in Chinese) [朱加民, 马正义, 郑春龙 2004 53 3248]
[14]	Lou S Y, Tang X Y, Li J 2001 Eur. Phys. J. B 22 473
[15]	Lou S Y 1995 J. Phys. Math. Gen. A 28 7227
[16]	Ruan H Y, Lou S Y 1997 J. Math. Phys. 38 3123
[17]	Lou S Y 1996 Commun. Theor. 26 487
[18]	Fang J P, Zheng C L, Chen L Q 2004 Commun. Theor. Phys. 42 175
[19]	Boiti M, Leon J J, Manna M, Pempinelli F 1989 Phys. Rev. Lett. A 63 1329
[20]	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 54 2990]
[21]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11 (in Chinese) [马松华, 吴小红, 方建平, 郑春龙 2008 57 11]
[22]	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 56 620]
[23]	Ma S H, Fang J P 2006 Acta Phys. Sin. 55 5611 (in Chinese) [马松华, 方建平 2006 55 5611]
[24]	Fang J P, Zheng C L 2005 Chin. Phys. B 4 670
[25]	Ma S H, Fang J P, Ren Q B, Yang Z 2012 Chin. Phys. B 21 050511
[26]	Lei Y, Ma S H, Fang J P 2013 Chin. Phys. B 22 010506
[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 59 4420]
[29]	Ma S H, Fang J P, Wu H Y 2013 Z. Naturforsch 68a 350
[30]	Dai C Q, Zhou G Q 2007 Chin. Phys. 16 1201
[31]	Ma Z Y, Ma S H 2012 Chin. Phys. B 21 030507
[32]	Chen Y M, Ma S H, Ma Z Y 2012 Chin. Phys. B 21 050510
[33]	Mei J Q, Zhang H Q 2005 Commun. Theor. Phys. 44 209
[34]	Boiti M, Leon J J, Manna M, Pempinelli F 1986 Inverse Problem 2 271
[35]	Zhang J F 2002 Commun. Theor. Phys. 37 277

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(2+1)维色散长波方程的新精确解及其复合波激发

New exact solutions and complex wave excitations for the (2+1)-dimensional dispersive long wave equation

摘要

Abstract

作者及机构信息

1.
龙岩学院物理系, 龙岩 364012;

2.
丽水学院物理系, 丽水 323000

Authors and contacts

1.
Department of Physics, Longyan University, Longyan 364012, China;

2.
Department of Physics, Lishui University, Lishui 323000, China

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(2+1)维色散长波方程的新精确解及其复合波激发

New exact solutions and complex wave excitations for the (2+1)-dimensional dispersive long wave equation

摘要

Abstract

作者及机构信息

1. 龙岩学院物理系, 龙岩 364012; 2. 丽水学院物理系, 丽水 323000

Authors and contacts

1. Department of Physics, Longyan University, Longyan 364012, China; 2. Department of Physics, Lishui University, Lishui 323000, China

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关于我们

1.
龙岩学院物理系, 龙岩 364012;

2.
丽水学院物理系, 丽水 323000

1.
Department of Physics, Longyan University, Longyan 364012, China;

2.
Department of Physics, Lishui University, Lishui 323000, China