构造非线性发展方程无穷序列复合型精确解的一种方法

套格图桑

doi:10.7498/aps.60.010202

摘要

为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Bcklund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义.

关键词:

To seek new infinite sequence complexiton solutions to nonlinear evolution equations(NEE(s)), the formula of nonlinear superposition of the solutions and Bcklund transformation of Riccati equation are presented, and as an illusrative exapmle, the generalized Boussinesq equation is chosen to obtain new infinite sequence complexiton solutions with the aid of symbolic computation system Mathematica, which includes complexiton solutions of hyperbolic function, triangular function type with rational function and hyperbolic function with triangular function. The method is of significance to construct infinite sequence complexiton solutions to other NEEs.

Keywords:

作者及机构信息

套格图桑

1.
内蒙古师范大学数学科学学院,呼和浩特 010022

基金项目: 国家自然科学基金(批准号:10461006),内蒙古自治区高等学校科学研究基金(批准号:NJZZ07031),内蒙古自治区自然科学基金(批准号:2010MS0111)和内蒙古师范大学自然科学研究计划(批准号:QN005023)资助的课题.

Authors and contacts

Taogetusang

1.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

参考文献

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[64]	Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 137
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施引文献

[1]	Zhang L, Zhang L F, Li C Y2008Chin.Phys.B 17 403
[2]
[3]
[4]	Wu H Y, Zhang L, Tan Y K, Zhou X T 2008Acta.Phys.Sin. 57 3312(in Chinese) [吴海燕、张亮、谭言科、周小滔 2008 57 3312]
[5]
[6]	Gao L, Xu W, Tang Y N, Shen J W 2007Acta.Phys.Sin. 561860(in Chinese)[高亮、徐伟、唐亚宁、申建伟 2007 56 1860]
[7]	Xu G Q, Li Z B 2003Acta.Phys.Sin. 521848(in Chinese)[徐桂琼、李志斌 2003 52 1848]
[8]
[9]
[10]	Wang M L 1995 Phys.Lett. A 199 169
[11]
[12]	Wu Y Q 2008 Acta.Phys.Sin. 57 5390(in Chinese)[吴勇旗 2008 57 5390]
[13]
[14]	He F, Guo Q B, Liu L 2007 Acta.Phys.Sin. 56 4326(in Chinese)[贺锋、郭启波、刘辽 2007 56 4326]
[15]	Zhang S Q, Li Z B 2003Acta.Phys.Sin. 52 1067(in Chinese)[张善卿、李志斌 2003 52 1067]
[16]
[17]	Wang Z, Li D S,Lu H F,Zhang H Q2005 Chin.Phys. 14 2158
[18]
[19]	Parkes E J, Duffy B R 1996Comput.Phys.Commun. 98288
[20]
[21]	Sirendaoreji, Sun J 2003Phys. Lett.A309387
[22]
[23]	Fu Z T, Liu S D, Liu S K 2003Commun.Theor.Phys.(Beijing,China) 39 531
[24]
[25]	Zhao X Q, Zhi H Y, Zhang H Q 2006Chin.Phys. 15 2202
[26]
[27]
[28]	Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[29]
[30]	Lu B, Zhang H Q 2008Chin.Phys.B 17 3974
[31]
[32]	Li H M 2005Chin.Phys. 14251
[33]
[34]	Zhu J M, Zheng C L, Ma Z Y 2004Chin.Phys. 132008
[35]	Taogetusang, Sirendaoerji 2006 Chin.Phys. 15 2809
[36]
[37]	Pan J T, Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese)[潘军廷、龚伦训 2007 56 5585]
[38]
[39]	Sirendaoerji2003 J.Modern.Phys. C 14 1075
[40]
[41]	Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta.Phys.Sin. 57 11(in Chinese) [马松华、吴小红、方建平、郑春龙 2008 57 11]
[42]
[43]
[44]	Ma S H,Fang J P,Zheng C L2008 Chin.Phys.B 172767
[45]
[46]	Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing, China) 41 1
[47]
[48]	Liu C S 2005 Acta.Phys.Sin. 544506(in Chinese)[刘成仕 2005 544506]
[49]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 521569(in Chinese)[李德生、张鸿庆 2003 521569]
[50]
[51]
[52]	Lu D C, Hong B J, Tian L X2006 Acta.Phys.Sin. 555617(in Chinese)[卢殿臣、烘宝剑、田立新 2006 555617]
[53]
[54]	Mao J J, Yang J R2005Acta.Phys.Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[55]
[56]	Ma S H, Fang J P 2006Acta.Phys.Sin. 555611(in Chinese) [马松华、方建平 2006 55 5611]
[57]	Fan E G 2000 Phys.Lett. A 277212
[58]
[59]
[60]	Chen Y, Li B, Zhang H Q 2003Chin.Phys. 12 940
[61]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003Chin.Phys. 121
[62]
[63]
[64]	Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 137
[65]
[66]	Li D S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 143
[67]
[68]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 39 647
[69]
[70]	L Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[71]	Bai C L 2003 Commun.Theor.Phys.(Beijing)40 147
[72]
[73]	Li D S, Zhang H Q 2004Chin.Phys. 13984

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