广义(3+1)维非线性Burgers系统孤波级数解

温朝晖; 莫嘉琪

doi:10.7498/aps.59.8311

摘要

研究了一类广义(3+1)维非线性Burgers系统.首先,利用同伦映射方法构造了相应的映射关系式.其次,利用迭代方法得到了扰动系统的一个孤波非行波的级数解.

关键词:

Burgers系统 /
非线性 /
孤波解

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.

Keywords:

作者及机构信息

温朝晖¹,
莫嘉琪²

(1)安徽财经大学应用数学研究所,蚌埠 233030; (2)安徽师范大学数学系,芜湖 241003

基金项目: 国家自然科学基金(批准号: 40876010)、中国科学院知识创新工程重要方向性项目(批准号: KZCX2-YW-Q03-08)、大气科学和地球流体力学数值模拟国家重点实验室基金和浙江省自然科学基金(批准号: Y6090164) 资助的课题.

Authors and contacts

Mo Jia-Qi¹,
Wen Zhao-Hui²

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

参考文献

[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 49 2113]
[5]	Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 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 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 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 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 55 13]
[12]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑、斯仁道尔吉 2006 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 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 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 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 58 695]
[36]	Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 58 7419]
[37]	Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[38]	Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 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 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

施引文献

[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 49 2113]
[5]	Fan E G 2000 Acta Phys. Sin. 49 1409 (in Chinese) [范恩贵 2000 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 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 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 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 55 13]
[12]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑、斯仁道尔吉 2006 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 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 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 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 58 695]
[36]	Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 58 7419]
[37]	Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[38]	Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 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 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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广义(3+1)维非线性Burgers系统孤波级数解

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

摘要

Abstract

作者及机构信息

(1)安徽财经大学应用数学研究所,蚌埠 233030; (2)安徽师范大学数学系,芜湖 241003

Authors and contacts

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

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广义(3+1)维非线性Burgers系统孤波级数解

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

摘要

Abstract

作者及机构信息

(1)安徽财经大学应用数学研究所,蚌埠 233030; (2)安徽师范大学数学系,芜湖 241003

Authors and contacts

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

参考文献

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