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Solitary wave series solution for generalized (3+1)-dimensional nonlinear Burgers system

Mo Jia-Qi Wen Zhao-Hui

Solitary wave series solution for generalized (3+1)-dimensional nonlinear Burgers system

Mo Jia-Qi, Wen Zhao-Hui
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  • A class of generalized (3+1)-dimensional nonlinear Burgers system is studied. Using the homotopic mapping method, the corresponding mapping expansions are constructed and using the iteration method the series solution of travelling wave for a solitary wave is obtained.
    • Funds:
    [1]

    Parkes E J, Duffy B R 1996 Comp. Phys. Commun. 98 288

    [2]

    Perturbation (Amsterdam: North-Holland Publishing Co.)

    [3]

    Wang M L 1995 Phys. Lett. A 199 169

    [4]

    Yan Z Y, Zhang H Q 2000 Acta Phys. Sin. 49 2113 (in Chinese) [闫振亚、 张鸿庆 2000 物理学报 49 2113]

    [5]

    Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 物理学报 49 1409]

    [6]

    Parkes E J, Duffy B R, Abbott P C 2001 Phys. Lett. A 295 280

    [7]

    Liu S K, Liu S D, Fu Z T 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适、 刘适达、 付遵涛 2001 物理学报 50 2068]

    [8]

    Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese) [刘式达、 付遵涛、 刘式适、 赵 强 2002 物理学报 51 718]

    [9]

    Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、 韩家骅、 史良马、 张 苗 2006 物理学报 55 3858]

    [10]

    Sirendaoerji, Sun J 2003 Phys. Lett. A 309 387

    [11]

    Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑、 斯仁道尔吉 2006 物理学报 55 13]

    [12]

    Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑、 斯仁道尔吉 2006 物理学报 55 3246]

    [13]

    Li X Z, Li X Y, Zhao L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese)] 李向正、 李修勇、 赵丽英、 张金良 2008 物理学报 57 2203]

    [14]

    Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448

    [15]

    Ying J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203

    [16]

    Fang J P, Zheng C L 2005 Chin. Phys. 14 670

    [17]

    Zhen Y B, Wang M L, Miao T D 2004 Phys. Lett. A 323 77

    [18]

    Li X Z, Zhang J L, Wang Y M, Wang M L 2004 Acta Phys. Sin. 53 4045 (in Chinese) [李向正、 张金良、 王跃明、 王明亮 2004 物理学报 53 4045]

    [19]

    Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417

    [20]

    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]

    [21]

    Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press)

    [22]

    He J H 2002 Approximate 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分析方法 (郑州: 河南科学技术出版社)]

    [23]

    Ni W M, Wei J C 2006 J. Differ. Eqs. 221 158

    [24]

    Bartier J P 2006 Asymp. Anal. 46 325

    [25]

    Libre J, da Silva P R 2007 J. Dyn. Differ. Eqs. 19 309

    [26]

    Guarguaglini F R, Natalini R 2007 Commun. Par. Differ. Eqs. 32 163

    [27]

    Sagon G 2008 Nonlinearity 21 1183

    [28]

    Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297

    [29]

    Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392

    [30]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

    [31]

    Chen J H 2009 Complex Var. Elliptic Eqs. 54 71

    [32]

    Mo J Q 2009 Adv. Math. 38 227

    [33]

    Mo J Q, Lin W T 2008 J. Syst. Sci. Compl. 20 119

    [34]

    Mo J Q, Wang H 2007 Acta Ecolog. Sin. 27 4366

    [35]

    Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 物理学报 58 695]

    [36]

    Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、 姚静荪 2009 物理学报 58 7419]

    [37]

    Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 物理学报 58 2930]

    [38]

    Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、 程 燕 2009 物理学报 58 4379]

    [39]

    Mo J Q, Lin Y W, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 物理学报 58 6692]

    [40]

    Mo J Q 2009 Chin. Phys. Lett. 26 010204

    [41]

    Mo J Q 2009 Chin Phys. Lett. 26 060202

    [42]

    Mo J Q 2009 Sci. China G 39 568

    [43]

    Mo J Q, Lin W T 2008 Chin. Phys. 17 370

    [44]

    Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230

    [45]

    Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193

    [46]

    Mo J Q 2009 Acta Math. Sci. 29 1

    [47]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 17 030202

    [48]

    Mo J Q 2010 Chin. Phys. B 17 010203

    [49]

    de Jager E M, Jiang F R 1996 The Theory of Singular

  • [1]

    Parkes E J, Duffy B R 1996 Comp. Phys. Commun. 98 288

    [2]

    Perturbation (Amsterdam: North-Holland Publishing Co.)

    [3]

    Wang M L 1995 Phys. Lett. A 199 169

    [4]

    Yan Z Y, Zhang H Q 2000 Acta Phys. Sin. 49 2113 (in Chinese) [闫振亚、 张鸿庆 2000 物理学报 49 2113]

    [5]

    Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 物理学报 49 1409]

    [6]

    Parkes E J, Duffy B R, Abbott P C 2001 Phys. Lett. A 295 280

    [7]

    Liu S K, Liu S D, Fu Z T 2001 Acta Phys. Sin. 50 2068 (in Chinese) [刘式适、 刘适达、 付遵涛 2001 物理学报 50 2068]

    [8]

    Liu S D, Fu Z T, Liu S K, Zhao Q 2002 Acta Phys. Sin. 51 718 (in Chinese) [刘式达、 付遵涛、 刘式适、 赵 强 2002 物理学报 51 718]

    [9]

    Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、 韩家骅、 史良马、 张 苗 2006 物理学报 55 3858]

    [10]

    Sirendaoerji, Sun J 2003 Phys. Lett. A 309 387

    [11]

    Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑、 斯仁道尔吉 2006 物理学报 55 13]

    [12]

    Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑、 斯仁道尔吉 2006 物理学报 55 3246]

    [13]

    Li X Z, Li X Y, Zhao L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese)] 李向正、 李修勇、 赵丽英、 张金良 2008 物理学报 57 2203]

    [14]

    Ying J P, Lou S Y 2003 Chin. Phys. Lett. 20 1448

    [15]

    Ying J P, Zheng C L, Zhu J M 2005 Commun. Theor. Phys. 44 203

    [16]

    Fang J P, Zheng C L 2005 Chin. Phys. 14 670

    [17]

    Zhen Y B, Wang M L, Miao T D 2004 Phys. Lett. A 323 77

    [18]

    Li X Z, Zhang J L, Wang Y M, Wang M L 2004 Acta Phys. Sin. 53 4045 (in Chinese) [李向正、 张金良、 王跃明、 王明亮 2004 物理学报 53 4045]

    [19]

    Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417

    [20]

    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]

    [21]

    Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press)

    [22]

    He J H 2002 Approximate 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分析方法 (郑州: 河南科学技术出版社)]

    [23]

    Ni W M, Wei J C 2006 J. Differ. Eqs. 221 158

    [24]

    Bartier J P 2006 Asymp. Anal. 46 325

    [25]

    Libre J, da Silva P R 2007 J. Dyn. Differ. Eqs. 19 309

    [26]

    Guarguaglini F R, Natalini R 2007 Commun. Par. Differ. Eqs. 32 163

    [27]

    Sagon G 2008 Nonlinearity 21 1183

    [28]

    Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297

    [29]

    Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392

    [30]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

    [31]

    Chen J H 2009 Complex Var. Elliptic Eqs. 54 71

    [32]

    Mo J Q 2009 Adv. Math. 38 227

    [33]

    Mo J Q, Lin W T 2008 J. Syst. Sci. Compl. 20 119

    [34]

    Mo J Q, Wang H 2007 Acta Ecolog. Sin. 27 4366

    [35]

    Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 物理学报 58 695]

    [36]

    Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、 姚静荪 2009 物理学报 58 7419]

    [37]

    Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 物理学报 58 2930]

    [38]

    Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、 程 燕 2009 物理学报 58 4379]

    [39]

    Mo J Q, Lin Y W, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 物理学报 58 6692]

    [40]

    Mo J Q 2009 Chin. Phys. Lett. 26 010204

    [41]

    Mo J Q 2009 Chin Phys. Lett. 26 060202

    [42]

    Mo J Q 2009 Sci. China G 39 568

    [43]

    Mo J Q, Lin W T 2008 Chin. Phys. 17 370

    [44]

    Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230

    [45]

    Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193

    [46]

    Mo J Q 2009 Acta Math. Sci. 29 1

    [47]

    Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 17 030202

    [48]

    Mo J Q 2010 Chin. Phys. B 17 010203

    [49]

    de Jager E M, Jiang F R 1996 The Theory of Singular

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  • Received Date:  11 January 2010
  • Accepted Date:  17 June 2010
  • Published Online:  05 June 2010

Solitary wave series solution for generalized (3+1)-dimensional nonlinear Burgers system

  • 1. (1)Depratment of Mathemtics, Anhui Normal University, Wuhu 241003, China; (2)Institute of Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China

Abstract: A class of generalized (3+1)-dimensional nonlinear Burgers system is studied. Using the homotopic mapping method, the corresponding mapping expansions are constructed and using the iteration method the series solution of travelling wave for a solitary wave is obtained.

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