Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

The variational iteration method for characteristic problem of strong damping generalized sine-Gordon equation

Xu Yong-Hong Shi Lan-Fang Mo Jia-Qi

Citation:

The variational iteration method for characteristic problem of strong damping generalized sine-Gordon equation

Xu Yong-Hong, Shi Lan-Fang, Mo Jia-Qi
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • A class of nonlinear strong damping sine-Gordon disturbed evolution differential equation is studied which appears widely in mathematics and mechanics. Firstly, we introduce a traveling wave transformation, and obtain the exact solution of degenerate equation. Then a functional calculating method for variational iteration is constructed, thus an iterative expansion is found. Finally, the approximate traveling wave analytic solutions for the original strong damping generalized sine-Gordon disturbed evolution equation are found. The arbitrary order approximate solutions, and the simple variational iteration method are obtained with higher accuracy. The approximate analytic solution can make up for the imperfection of the simple numerical simulation solution.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11202106), the Fundamental Research Funds for the Central Universities, China (Grant No. 2232012D3-34), the Natural Science Foundation of the Education Department of Anhui Province, China (Grant No. KJ2014A151) and the Natural Sciences Foundation from the Universities of Jiangsu Province, China (Grant No. 13KJB170016).
    [1]

    Parkes E J 2008 Chaos Solitons Fractals 38 154

    [2]

    Sirendaoreji J S 2003 Phys. Lett. A 309 387

    [3]

    McPhaden M J, Zhang D 2002 Nature 415 603

    [4]

    Gu D F 1997 Science 275 805

    [5]

    Wu J P 2011 Chin. Phys. Lett. 28 060207

    [6]

    Zuo J M, Zhang Y M 2011 Chin. Phys. B 20 010205

    [7]

    Pang J, Jin L H, Zhao Q 2012 Acta Phys. Sin. 61 140201 (in Chinese) [庞晶, 靳玲花, 赵强 2012 物理学报 61 140201]

    [8]

    Xin P, Liu X Q, Zhang L L 2011 Chin. Phys. Lett. 28 020201

    [9]

    Li Ning, Liu Xi 2013 Acta Phys. Sin. 62 160203 (in Chinese) [李宁, 刘希 2013 物理学报 62 160203]

    [10]

    Xu Y H, Lin W T, Xu H, Yao J S, Mo J Q 2012 J. Lanzhou Univ. 48 100 (in Chinese) [许永红, 林万涛, 徐惠, 姚静荪, 莫嘉琪 2012 兰州大学学报 48 100]

    [11]

    Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta. Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 物理学报 62 010201]

    [12]

    Mo Jiaqi 2009 Science in China, Ser. G 52 1007

    [13]

    Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203

    [14]

    Mo J Q 2010 Chin. Phys. 19 010203

    [15]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. 19 030202

    [16]

    2011 Commun Theor. Phy. 55 387

    [17]

    Mo J Q, Lin W T 2011 J. Sys. Sci. Complexity 24 271

    [18]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205

    [19]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 010208

    [20]

    He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 郑州: 河南科学技术出版社]

    [21]

    Lebedev L P, Cloud M J 2003 The Calculus of Variations and Functional Analysis with Optimal Control and Applications in Mechanics (New York: World Scientific)

    [22]

    de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)

    [23]

    Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problem, (Basel: Birkhauserm Verlag AG)

    [24]

    He J H 1999 J. Non-Linear Mech 34 699

    [25]

    He J H 2000 Appl. Math. Comput 114 115

    [26]

    He J H 2004 Chaos, Solitons & Fractals 19 847

    [27]

    He J H, Wu X H 2006 Chaos, Solitons & Fractals 29 108

    [28]

    He J H 2007 Chaos, Solitons & Fractals 34 1430

    [29]

    He J H, Wu G C 2010 Nonlinear Sci. Lett. A 1 1

    [30]

    He J H 2010 J. Nonlinear Scoences and Nimweical Simulation 11 555

    [31]

    Wang Q, Fu F H 2012 Int. J. Engineering and Manufacturing 2 36

  • [1]

    Parkes E J 2008 Chaos Solitons Fractals 38 154

    [2]

    Sirendaoreji J S 2003 Phys. Lett. A 309 387

    [3]

    McPhaden M J, Zhang D 2002 Nature 415 603

    [4]

    Gu D F 1997 Science 275 805

    [5]

    Wu J P 2011 Chin. Phys. Lett. 28 060207

    [6]

    Zuo J M, Zhang Y M 2011 Chin. Phys. B 20 010205

    [7]

    Pang J, Jin L H, Zhao Q 2012 Acta Phys. Sin. 61 140201 (in Chinese) [庞晶, 靳玲花, 赵强 2012 物理学报 61 140201]

    [8]

    Xin P, Liu X Q, Zhang L L 2011 Chin. Phys. Lett. 28 020201

    [9]

    Li Ning, Liu Xi 2013 Acta Phys. Sin. 62 160203 (in Chinese) [李宁, 刘希 2013 物理学报 62 160203]

    [10]

    Xu Y H, Lin W T, Xu H, Yao J S, Mo J Q 2012 J. Lanzhou Univ. 48 100 (in Chinese) [许永红, 林万涛, 徐惠, 姚静荪, 莫嘉琪 2012 兰州大学学报 48 100]

    [11]

    Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta. Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 物理学报 62 010201]

    [12]

    Mo Jiaqi 2009 Science in China, Ser. G 52 1007

    [13]

    Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203

    [14]

    Mo J Q 2010 Chin. Phys. 19 010203

    [15]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. 19 030202

    [16]

    2011 Commun Theor. Phy. 55 387

    [17]

    Mo J Q, Lin W T 2011 J. Sys. Sci. Complexity 24 271

    [18]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205

    [19]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 010208

    [20]

    He J H 2002 Approximate Nonlinear Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese) [何吉欢 2002 工程和科学计算中的近似非线性分析方法 郑州: 河南科学技术出版社]

    [21]

    Lebedev L P, Cloud M J 2003 The Calculus of Variations and Functional Analysis with Optimal Control and Applications in Mechanics (New York: World Scientific)

    [22]

    de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)

    [23]

    Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problem, (Basel: Birkhauserm Verlag AG)

    [24]

    He J H 1999 J. Non-Linear Mech 34 699

    [25]

    He J H 2000 Appl. Math. Comput 114 115

    [26]

    He J H 2004 Chaos, Solitons & Fractals 19 847

    [27]

    He J H, Wu X H 2006 Chaos, Solitons & Fractals 29 108

    [28]

    He J H 2007 Chaos, Solitons & Fractals 34 1430

    [29]

    He J H, Wu G C 2010 Nonlinear Sci. Lett. A 1 1

    [30]

    He J H 2010 J. Nonlinear Scoences and Nimweical Simulation 11 555

    [31]

    Wang Q, Fu F H 2012 Int. J. Engineering and Manufacturing 2 36

  • [1] Zheng Lai-Yun, Zhao Bing-Xin, Yang Jian-Qing. Bifurcation and nonlinear evolution of convection in binary fluid mixtures with weak Soret effect. Acta Physica Sinica, 2020, 69(7): 074701. doi: 10.7498/aps.69.20191836
    [2] Ning Li-Zhong, Hu Biao, Ning Bi-Bo, Tian Wei-Li. Partition and growth of convection patterns in Poiseuille-Rayleigh-Bnard flow. Acta Physica Sinica, 2016, 65(21): 214401. doi: 10.7498/aps.65.214401
    [3] Taogetusang, Yi Li-Na. New infinite sequence solutions to equations of sine-Gordon type. Acta Physica Sinica, 2014, 63(21): 210202. doi: 10.7498/aps.63.210202
    [4] Ouyang Cheng, Yao Jing-Sun, Shi Lan-Fang, Mo Jia-Qi. Solitary wave solution for a class of dusty plasma. Acta Physica Sinica, 2014, 63(11): 110203. doi: 10.7498/aps.63.110203
    [5] Shi Lan-Fang, Zhu Min, Zhou Xian-Chun, Wang Wei-Gang, Mo Jia-Qi. The solitary traveling wave solution for a class of nonlinear evolution equations. Acta Physica Sinica, 2014, 63(13): 130201. doi: 10.7498/aps.63.130201
    [6] Zhao Long, Yang Ji-Ping, Zheng Yan-Hong. Modulation of nonlinear coupling on the synchronization induced by linear coupling. Acta Physica Sinica, 2013, 62(2): 028701. doi: 10.7498/aps.62.028701
    [7] Yao Xiong-Liang, Ye Xi, Zhang A-Man. Cavitation bubble in compressible fluid subjected to traveling wave. Acta Physica Sinica, 2013, 62(24): 244701. doi: 10.7498/aps.62.244701
    [8] Gao Mei-Ru, Chen Huai-Tang. Hybrid solutions of three functions to the (2+1)-dimensional sine-Gordon equation. Acta Physica Sinica, 2012, 61(22): 220509. doi: 10.7498/aps.61.220509
    [9] Taogetusang. New infinite sequences exact solutions to sine-Gordon-type equations. Acta Physica Sinica, 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
    [10] Zhang Jian-Wen, Li Jin-Feng, Wu Run-Heng. Global attractor of strongly damped nonlinearthermoelastic coupled rod system. Acta Physica Sinica, 2011, 60(7): 070205. doi: 10.7498/aps.60.070205
    [11] Su Jun, Xu Wei, Duan Dong-Hai, Xu Gen-Jiu. New explicit exact solution of one type of the sine-Gordon equation with self-consistent source. Acta Physica Sinica, 2011, 60(11): 110203. doi: 10.7498/aps.60.110203
    [12] Taogetusang, Sirendaoerji. New exact solutions to (n+1)-dimensional double sine-Gordon equation. Acta Physica Sinica, 2010, 59(8): 5194-5201. doi: 10.7498/aps.59.5194
    [13] Mo Jia-Qi. Analytic solution for a class of generalized Sine-Gordon perturbation equation. Acta Physica Sinica, 2009, 58(5): 2930-2933. doi: 10.7498/aps.58.2930
    [14] Ning Li-Zhong, Qi Xin, Yu Li, Zhou Yang. Defect structures of Rayleigh-Benard travelling wave convection in binary fluid mixtures. Acta Physica Sinica, 2009, 58(4): 2528-2534. doi: 10.7498/aps.58.2528
    [15] Zhang Jian-Wen, Wang Dan-Xia, Wu Run-Heng. Global solutions for a kind of generalized Sine-Gordon equation with strong damping. Acta Physica Sinica, 2008, 57(4): 2021-2025. doi: 10.7498/aps.57.2021
    [16] Mao Jie-Jian, Yang Jian-Rong. New solitary wave-like solution and exact solution of variable coefficient KP equation. Acta Physica Sinica, 2005, 54(11): 4999-5002. doi: 10.7498/aps.54.4999
    [17] TANG YI, YAN JIA-REN, ZHANG KAI-WANG, CHEN ZHEN-HUA. PERTURBATION THEORY FOR SINE-GORDON EQUATION. Acta Physica Sinica, 1999, 48(3): 480-484. doi: 10.7498/aps.48.480
    [18] Xu Bo-Wei, Chen Zhi-Jian, Ding Guo-Hui, Zhang Yu-Mei. . Acta Physica Sinica, 1995, 44(2): 189-195. doi: 10.7498/aps.44.189
    [19] XU BO-WEI, ZHANG YU-MEI, LU WEN-FA. SINE-GORDON MODEL AND GAUSSIAN WAVE FUNCTIONAL. Acta Physica Sinica, 1993, 42(10): 1573-1579. doi: 10.7498/aps.42.1573
    [20] WANG PEI, HOU BO-YUAN, HOU BO-YU, GUO HAN-YING. DUAL SYMMETRY OF CHIRAL MODEL AND GEOMETRICAL CORRESPONDENCE BETWEEN CHIRAL FIELD AND SINE-GORDON EQUATION. Acta Physica Sinica, 1984, 33(3): 294-301. doi: 10.7498/aps.33.294
Metrics
  • Abstract views:  5435
  • PDF Downloads:  660
  • Cited By: 0
Publishing process
  • Received Date:  24 July 2014
  • Accepted Date:  14 August 2014
  • Published Online:  05 January 2015

/

返回文章
返回