几种辅助方程与非线性发展方程的无穷序列精确解

套格图桑

doi:10.7498/aps.60.050201

摘要

本文为了获得非线性发展方程新的无穷序列精确解,给出了几种辅助方程的Böcklund变换和解的非线性叠加公式,并构造了一些非线性发展方程新的无穷序列精确解,其中包括无穷序列Jacobi椭圆函数解、无穷序列双曲函数解和无穷序列三角函数解.该方法在构造非线性发展方程无穷序列精确解方面具有普遍意义.

关键词:

To seek infinite sequence exact solutions of nonlinear evolution equations, the Böcklund transformation of the solutions to some auxiliary equations and the formula of nonlinear superimposition of solutions are presented for constructing infinite sequence exact solutions to nonlinear evolution equations, which include infinite sequence Jacobi elliptic function solutions, infinite sequence hyperbolic function solutions and infinite sequence trigonomical function solutions. The method is of significance to the search into infinite sequence exact solutions of other nonlinear evolution equations.

Keywords:

auxiliary equation method /
formula of nonlinear superposition of solution /
infinite sequence solution /
nonlinear evolution equation

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: 国家自然科学基金资助(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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[46]	Li J B 2007 Scie.Chin.Ser.Math.A 50 153
[47]	Li H M 2003 Commun.Theor.Phys.(Beijing) 39 395
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[50]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 2809
[51]	Liu C S 2005 Chin.Phys. 14 1710
[52]	Zhu J M,Zheng C L,Ma Z Y 2004 Chin.Phys. 13 2008
[53]	Fu Z T,Liu S D,Liu S K 2003 Commun.Theor.Phys.(Beijing) 39 531
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[56]	Liu C S,Du X H 2005 Acta.Phys.Sin. 54 1039(in Chinese)[刘成仕、杜兴华 2005 54 1039]
[57]	Pan J T,Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese) [潘军廷、龚伦训 2007 56 5585]
[58]	Taogetusang, Sirendaoerji 2008 Acta.Phys.Sin. 57 1295(in Chinese) [套格图桑、斯仁道尔吉 2008 57 1295]
[59]	Sirendaoerji,Sun J 2003 Phys.Lett.A 309 387
[60]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 3246(in Chinese) [套格图桑、斯仁道尔吉 2006 55 3246]
[61]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 1143
[62]	Taogetusang, Sirendaoerji 2007 Acta.Phys.Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 56 627]
[63]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 55 13]
[64]	Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese) [毛杰健、杨建荣 2005 54 4999]
[65]	Fu Z T,Liu S K,Liu S D 2003 Commun.Theor.Phys.(Beijing) 39 27
[66]	Yu J,Ke Y Q,Zhang W J 2004 Commun.Theor.Phys.(Beijing) 40 493
[67]	Sirendaoerji,Sun J 2002 Phys.Lett.A 298 133
[68]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 52 2373]
[69]	Fu Z T, Liu S K, Liu S D 2004 Acta.Phys.Sin. 53 343(in Chinese) [付遵涛、刘式适、刘式达 2004 53 343]
[70]	Zhao C H, Sheng Z M 2004 Acta.Phys.Sin. 53 1629(in Chinese)[赵长海、盛正卯 2004 53 1629]
[71]	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]
[72]	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]
[73]	Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese) [套格图桑、斯仁道尔吉 2010 59 4413]
[74]	Narenmandula 2002 Acta.Phys.Sin. 51 1671(in Chinese)[那仁满都拉 2002 51 1671]
[75]	Narenmandula,Wang K X 2003 Acta.Phys.Sin. 52 1565(in Chinese)[那仁满都拉、王克协 2003 52 1565]

施引文献

[1]	Zabusky N, Kruskal M D 1965 Phys.Rev.Lett. 15 240
[2]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys.Rev.Lett. 19 1095
[3]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Comn.Pure.Appi.Math. 27 97
[4]	Miura R M 1976 SIAM.Rev. 18 412
[5]	Wang M L 1995 Phys.Lett.A 199 169
[6]	Parkes E J, Duffy B R 1996 Comput.Phys.Commun. 98 288
[7]	Fan E G 2000 Phys.Lett.A 277 212
[8]	Chen Y, Li B, Zhang H Q 2003 Chin.Phys. 12 940
[9]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin.Phys. 12 1
[10]	Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 137
[11]	Li D S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 143
[12]	Li D S, Zhang H Q 2004 Chin.Phys. 13 984
[13]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[14]	Chen H T, Zhang H Q 2004 Commun.Theor.Phys.(Beijing) 42 497
[15]	Xie F D, Chen J, Lü Z S 2005 Commun.Theor.Phys.(Beijing) 43 585
[16]	Xie F D,Yuan Z T 2005 Commun.Theor.Phys.(Beijing) 43 39
[17]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 647
[18]	Lü Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[19]	Xie F D, Gao X S 2004 Commun.Theor.Phys.(Beijing) 41 353
[20]	Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing) 41 1
[21]	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]
[22]	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]
[23]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 1569(in Chinese) [李德生、张鸿庆 2003 52 1569]
[24]	Zeng X, Zhang H Q 2005 Acta.Phys.Sin. 54 504(in Chinese)[曾昕、张鸿庆 2005 54 504]
[25]	Zhi H Y, Wang Q, Zhang H Q 2005 Acta.Phys.Sin. 54 1002(in Chinese)[智红燕、王琪、张鸿庆 2005 54 1002]
[26]	Pan J T, Gong L X 2008 Chin.Phys. B 17 399
[27]	Jiao X Y, Wang J H,Zhang H Q 2005 Commun.Theor.Phys.(Beijing)44 407
[28]	Liu Y P, Li Z B 2003 Chin.Phys.Lett. 20 317
[29]	Xu G Q, Li Z B 2003 Commun.Theor.Phys.(Beijing) 39 39
[30]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 55 6214]
[31]	Gao L, Xu W,Tang Y N, Shen J W 2007 Acta.Phys.Sin. 56 1860(in Chinese)[高亮、徐伟、唐亚宁、申建伟 2007 56 1860]
[32]	Li Z L 2009 Chin.Phys.B 18 4074
[33]	Lu D C, Hong B J, Tian L X 2006 Acta.Phys.Sin. 55 5617(in Chinese)[卢殿臣、烘宝剑、田立新2006 55 5617]
[34]	Huang D J, Zhang H Q 2004 Acta.Phys.Sin. 53 2434(in Chinese)[黄定江、张鸿庆 2004 53 2434]
[35]	Zhang S Q, Li Z B 2002 Acta.Phys.Sin. 51 2197(in Chinese)[张善卿、李志斌 2002 51 2197]
[36]	Zhao X Q, Tang D B,Wang L M,Zhang Y M 2003 Acta.Phys.Sin. 52 1827(in Chinese)[赵熙强、唐登斌、王利民、张耀明 2002 51 2197]
[37]	Wang Z,Li D S, Lu H F,Zhang H Q 2005 Chin.Phys. 14 2158
[38]	Li D S, Zhang H Q 2006 Acta.Phys.Sin. 55 1565(in Chinese)[李德生、张鸿庆 2006 55 1565]
[39]	Yong X L, Zhang H Q 2005 Acta.Phys.Sin. 54 2514(in Chinese)[雍雪林、张鸿庆 2005 54 2514]
[40]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[41]	Lu B, Zhang H Q 2008 Chin.Phys.B 17 3974
[42]	Wang Z, Zhang H Q 2006 Chin.Phys. 15 2210
[43]	Zhang J L,Ren D F,Wang M L,Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[44]	Zhang L,Zhang L F,Li C Y 2008 Chin.Phys.B 17 403
[45]	Zhao X Q,Zhi H Y,Zhang H Q 2006 Chin.Phys. 15 2202
[46]	Li J B 2007 Scie.Chin.Ser.Math.A 50 153
[47]	Li H M 2003 Commun.Theor.Phys.(Beijing) 39 395
[48]	Li H M 2005 Chin.Phys. 14 251
[49]	Li H M 2002 Chin.Phys. 11 1111
[50]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 2809
[51]	Liu C S 2005 Chin.Phys. 14 1710
[52]	Zhu J M,Zheng C L,Ma Z Y 2004 Chin.Phys. 13 2008
[53]	Fu Z T,Liu S D,Liu S K 2003 Commun.Theor.Phys.(Beijing) 39 531
[54]	Fu Z T,Liu S K,Liu S D 2004 Commun.Theor.Phys.(Beijing) 42 343
[55]	Wu H Y,Zhang L,Tan Y K, Zhou X T 2008 Acta.Phys.Sin. 57 3312(in Chinese)[吴海燕、张亮、谭言科、周小滔 2008 57 3312]
[56]	Liu C S,Du X H 2005 Acta.Phys.Sin. 54 1039(in Chinese)[刘成仕、杜兴华 2005 54 1039]
[57]	Pan J T,Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese) [潘军廷、龚伦训 2007 56 5585]
[58]	Taogetusang, Sirendaoerji 2008 Acta.Phys.Sin. 57 1295(in Chinese) [套格图桑、斯仁道尔吉 2008 57 1295]
[59]	Sirendaoerji,Sun J 2003 Phys.Lett.A 309 387
[60]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 3246(in Chinese) [套格图桑、斯仁道尔吉 2006 55 3246]
[61]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 1143
[62]	Taogetusang, Sirendaoerji 2007 Acta.Phys.Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 56 627]
[63]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 55 13]
[64]	Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese) [毛杰健、杨建荣 2005 54 4999]
[65]	Fu Z T,Liu S K,Liu S D 2003 Commun.Theor.Phys.(Beijing) 39 27
[66]	Yu J,Ke Y Q,Zhang W J 2004 Commun.Theor.Phys.(Beijing) 40 493
[67]	Sirendaoerji,Sun J 2002 Phys.Lett.A 298 133
[68]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 52 2373]
[69]	Fu Z T, Liu S K, Liu S D 2004 Acta.Phys.Sin. 53 343(in Chinese) [付遵涛、刘式适、刘式达 2004 53 343]
[70]	Zhao C H, Sheng Z M 2004 Acta.Phys.Sin. 53 1629(in Chinese)[赵长海、盛正卯 2004 53 1629]
[71]	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]
[72]	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]
[73]	Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese) [套格图桑、斯仁道尔吉 2010 59 4413]
[74]	Narenmandula 2002 Acta.Phys.Sin. 51 1671(in Chinese)[那仁满都拉 2002 51 1671]
[75]	Narenmandula,Wang K X 2003 Acta.Phys.Sin. 52 1565(in Chinese)[那仁满都拉、王克协 2003 52 1565]

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