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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.
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Keywords:
- Burgers system /
- nonlinear /
- solitary wave solution
[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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