Variational principles for two kinds of extended Korteweg–de Vries equations

doi:10.1088/1674-1056/20/9/090401

中国物理B ›› 2011, Vol. 20 ›› Issue (9): 90401-090401.doi: 10.1088/1674-1056/20/9/090401

Variational principles for two kinds of extended Korteweg–de Vries equations

曹小群, 宋君强, 张卫民, 赵军

School of Computer Science, National University of Defense Technology, Changsha 410073, China

收稿日期:2010-12-29 修回日期:2011-04-06 出版日期:2011-09-15 发布日期:2011-09-15

Variational principles for two kinds of extended Korteweg–de Vries equations

Cao Xiao-Qun(曹小群)^†, Song Jun-Qiang(宋君强), Zhang Wei-Min(张卫民), and Zhao Jun(赵军)

School of Computer Science, National University of Defense Technology, Changsha 410073, China

Received:2010-12-29 Revised:2011-04-06 Online:2011-09-15 Published:2011-09-15

摘要/Abstract

摘要： Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg—de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.

Abstract: Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg—de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.

Key words: He's semi-inverse method, variational principles, oceanic internal wave, atmospheric long wave

中图分类号: (Canonical formalism, Lagrangians, and variational principles)

04.20.Fy

92.10.hf (Planetary waves, Rossby waves) 92.10.hj (Internal and inertial waves)

曹小群, 宋君强, 张卫民, 赵军. Variational principles for two kinds of extended Korteweg–de Vries equations[J]. 中国物理B, 2011, 20(9): 90401-090401.

Cao Xiao-Qun(曹小群), Song Jun-Qiang(宋君强), Zhang Wei-Min(张卫民), and Zhao Jun(赵军) . Variational principles for two kinds of extended Korteweg–de Vries equations[J]. Chin. Phys. B, 2011, 20(9): 90401-090401.

参考文献 37

[1]	Lü M Z and Peng Y Q 1990 Dynamical Meteorology (Beijing: Meteorology Press) (in Chinese)
[2]	Wang P and Dai X G 2005 Acta Phys. Sin. 54 4961 (in Chinese)
[3]	Liang L W and Li X D 2009 Acta Phys. Sin. 58 2159 (in Chinese)
[4]	Yang J and Zhao Q 2010 Acta Phys. Sin. 59 750 (in Chinese)
[5]	Da C J and Chou J F 2008 Acta Phys. Sin. 57 2595 (in Chinese)
[6]	Song J and Yang L G 2009 Chin. Phys. B 18 2873
[7]	Song J and Yang L G 2010 Acta Phys. Sin. 59 3309 (in Chinese)
[8]	Lamb K and Yan L 1996 J. Phys. Oceanogr. 26 2712
[9]	Liu A K and Chang Y S 1998 J. Geophys. Res. 103 7995
[10]	Holloway P E and Pelinovsky E 1999 J. Geophys. Res. 104 18333
[11]	Ablowitz M J and Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
[12]	Gardner C S and Greene J M 1967 Phys. Rev. Lett. 19 1095
[13]	He J H 2005 Chaos Soliton. Fract. 26, 695
[14]	He J H 1999 Int. J. Nonlin. Mech. 34, 699
[15]	He J H 2005 Phys. Lett. A 335 182
[16]	He J H 2006 Int. J. Mod. Phys. B 20 1141
[17]	Fan E G and Zhang H Q 1998 Acta Phys. Sin. 47 353 (in Chinese)
[18]	Liu S K, Fu Z T and Liu S D 2002 Acta Phys. Sin. 51 10 (in Chinese)
[19]	Li B A and Wang M L 2005 Chin. Phys. 14 1698
[20]	Li H M 2005 Chin. Phys. 14 251
[21]	Wang Z and Zhang H Q 2006 Chin. Phys. 15 2210
[22]	Lou S Y and Qu C Z 2006 Chin. Phys. 15 2765
[23]	Taogetusang and Sirendaoerji 2006 Chin. Phys. 15 2809
[24]	Wang Z Y and Chen A H 2007 Chin. Phys. 16 1233
[25]	Chen Y and Fan E G 2007 Chin. Phys. 16 6
[26]	He J H and Wu X H 2006 Chaos Soliton. Fract. 30 700
[27]	He J H 2008 Int. J. Mod. Phys. B 22 3487
[28]	He J H 1997 Int. J. Turbo. Jet-Eng. 14 23
[29]	He J H 2000 Appl. Math. Mech. 21 797
[30]	He J H 2004 Chaos Soliton. Fract. 19, 847
[31]	He J H 2005 Phys. Lett. A 335 182
[32]	He J H 2007 Phys. Lett. A 371 39
[33]	He J H and Lee E W M 2009 Phys. Lett. A 373 1644
[34]	Zheng C B, Liu B, Wang Z J and Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1369
[35]	Zheng C B, Liu B, Wang Z J and Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1523
[36]	Craig W, Guyenne P and Kalisch H 2005 Comm. Pure Appl. Math. 58 1587
[37]	Craig W, Guyenne P and Kalisch H 2007 Proc. of OMAE07 461 839

Variational principles for two kinds of extended Korteweg–de Vries equations

Variational principles for two kinds of extended Korteweg–de Vries equations

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 37

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	徐鑫鑫, 张毅. A new type of adiabatic invariants for disturbednon-conservative nonholonomic system[J]. 中国物理B, 2019, 28(12): 120402-120402.
[2]	朱孟斌, 张卫民, 曹小群, 余意. Impact of GNSS radio occultation bending angle data assimilation in YH4DVAR system[J]. 中国物理B, 2014, 23(6): 69202-069202.
[3]	曹小群,宋君强,朱小谦,张理论,张卫民,赵军. [J]. 中国物理B, 2012, 21(2): 20203-020203.
[4]	陈松柏, 荆继良. Entropy and topology of the Kerr-de Sitter black hole[J]. 中国物理B, 2002, 11(1): 87-90.
[5]	李仁杰, 乔永芬, 刘洋. Integrating factors and conservation theorems for Hamilton's canonical equations of motion of variable mass nonholonomic nonconservative dynamical systems[J]. 中国物理B, 2002, 11(8): 760-764.
[6]	陈菊华, 荆继良, 王永久. THERMODYNAMICS OF THE SLOWLY ROTATING KERR-NEWMAN BLACK HOLE IN THE GRAND CANONICAL ENSEMBLE[J]. 中国物理B, 2001, 10(6): 467-474.