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本文为了构造非线性发展方程的无穷序列尖峰精确解,给出了Riccati方程的Bäcklund 变换和解的非线性叠加公式,并借助符号计算系统Mathematica,用Degasperis-Procesi方程为应用实例,构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解.
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关键词:
- Riccati方程 /
- 解的非线性叠加公式 /
- 尖峰孤立波解 /
- Degasperis-Procesi 方程
To construct infinite sequence peak solitary wave solutions to nonlinear evolution equations, Bäcklund transformation of Riccati equation and nonlinear superposition formula of the solutions are introduced, then Degasperis-Procesi equation is taken as an example and infinite sequence peak solitary wave solutions and periodic solutions of the equation are obtained with the help of symbolic computation system Mathematica.-
Keywords:
- Riccati equation /
- nonlinear superposition formula of the solutions /
- peak solitary wave solution /
- Degasperis-Procesi equation
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[36] Taogetusang 2010 Acta.Phys.Sin. 59 6712(in Chinese)[套格图桑、斯仁道尔吉 2010 59 6712]
[37] Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese)[套格图桑、斯仁道尔吉 2010 59 4413]
[38] Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 5194(in Chinese)[套格图桑、斯仁道尔吉 2010 59 5194]
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[1] Russell J S. Reports on waves, Edinburgh: Proc. Royal. Soc.,1844,311
[2] Korteweg D J, de Vries G 1895 Phil.Mag.39 422
[3] Zabusky N, Kruskal M D 1965 Phys.Rev.Lett.15 240
[4] Camassa R,Holm D D 1993 Phys. Rev. Lett.71 1661
[5] Alber M S,Camassa R 1994 Lett.Math.Phys. 32 137
[6] Clarkson P A,Mansfield E L,Priestley T J 1997 Math.Comput.Modelling 25 195
[7] Xin Z P,Zhang P 2000 Comm.Pure.Appl.Math.53 1411
[8] Michael Fisher,Jeremy Schiff 1999 Phys.Lett. A 259 371
[9] Adrian Constantin,Waner A Atrauss 2000 Comm.Pure.Appl.Math.53 603
[10] Tian L X, Xu G,Liu Z R 2002 Appl.Math.Mechanics 23 497(in Chinese)[田立新、许 刚、刘曾荣 2002 应用数学和力学 23 497]
[11] Dullin H R,Gottwald G A,Holm D D 2002 Phys.Rev.Lett.87 4501
[12] Guo B L, Liu Z R 2003 Science in China A 33 325 (in Chinese)[郭柏灵、刘正荣 2003 中国科学 A 33 325]
[13] Yin J L, Tian L X 2009 Acta.Phys.Sin.58 3632(in Chinese)[殷久利、田立新 2009 58 3632]
[14] Yu L Q, Tian L X 2006 Math.Practice.Theory.36 261(in Chinese)[余丽琴、田立新 2006 数学的实践与认识 36 261]
[15] Yu L Q, Tian L X 2005 Pure.Appl.Math. 21 310(in Chinese)[余丽琴、田立新 2005 纯粹数学与应用数学 21 310]
[16] Fan E G 2000 Phys.Lett. A 277 212
[17] Chen Y, Li B, Zhang H Q 2003 Chin.Phys. 12 940
[18] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin.Phys. 12 1
[19] Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. 40 137
[20] Li D S, Zhang H Q 2003 Commun.Theor.Phys. 40 143
[21] Li D S, Zhang H Q 2004 Chin.Phys. 13 984
[22] Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[23] Chen H T, Zhang H Q 2004 Commun.Theor.Phys. 42 497
[24] Xie F D, Chen J, Lü Z S 2005 Commun.Theor.Phys. 43 585
[25] Xie F D,Yuan Z T 2005 Commun.Theor.Phys. 43 39
[26] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. 39 647
[27] Lü Z S, Zhang H Q 2003 Commun.Theor.Phys. 39 405
[28] Xie F D, Gao X S 2004 Commun.Theor.Phys. 41 353
[29] Chen Y, Li B 2004 Commun.Theor.Phys. 41 1
[30] Ma S H, Fang J P, Zhu H P 2007 Acta.Phys.Sin.56 4319(in Chinese)[马松华、方建平、朱海平 2007 56 4319]
[31] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta.Phys.Sin.57 11(inChinese)[马松华、吴小红、方建平、郑春龙 2008 57 11]
[32] Pan Z H, Ma S H, Fang J P 2010 Chin.Phys.B 19 100301
[33] Qiang J Y, Ma S H, Fang J P 2010 Chin.Phys. B 19 090305
[34] Taogetusang, Sirendaoerji, Li S M 2010 Chin.Phys.B 19 080303
[35] Taogetusang, Sirendaoerji,Wang Q P 2009 Acta Sci.J.Nat.Univ.NeiMongol 38 387(in Chinese) [套格图桑、斯仁道尔吉、王庆鹏 2009 内蒙古师范大学学报 38 387]
[36] Taogetusang 2010 Acta.Phys.Sin. 59 6712(in Chinese)[套格图桑、斯仁道尔吉 2010 59 6712]
[37] Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese)[套格图桑、斯仁道尔吉 2010 59 4413]
[38] Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 5194(in Chinese)[套格图桑、斯仁道尔吉 2010 59 5194]
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