K(m,n)方程与B(m,n)方程的无穷序列新精确解

白玉梅; 套格图桑; 韩元春

doi:10.7498/aps.61.200205

摘要

进一步研究了辅助方程法,给出了几种常用辅助方程的新解、 Bcklund变换和解的非线性叠加公式. 在此基础上,根据m和n的不同情况,利用变换和直接积分相结合的方法, 获得了K (m,n)方程与B (m,n)方程的无穷序列新精确解. 这里包括无穷序列光滑孤立子解、无穷序列尖峰孤立子解和无穷序列紧孤立子解.

关键词:

New solutions of several kinds of auxiliary equations, Bcklund transformation and nonlinear superposition formula of the solutions are presented by studying a highly auxiliary equation method. Based on this and different m and n, the method of combining transformation and direct integration is used to obtain infinite sequence new exact solutions of K(m,n) equation and B(m,n) equation, which include infinite sequence smooth soliton solutions, peak soliton solutions and compact soliton solutions.

Keywords:

作者及机构信息

1.
内蒙古民族大学数学学院, 通辽 028043;

2.
内蒙古师范大学数学科学学院, 呼和浩特 010022;

3.
内蒙古民族大学物理与电子信息学院, 通辽 028043

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: NJZY12031)和内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.

Authors and contacts

1.
College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China;

2.
College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China;

3.
College of Physics and Electronics, Inner Mongolia University for Nationalities, Tongliao 028043, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10862003), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZY12031), and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2010MS0111).

参考文献

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施引文献

[1]	Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[2]	Boyd J P 1997 Appl. Math. Comput. 81 173
[3]	Guo B L, Liu Z R 2003 Sci. China A 33 325 (in Chinese) [郭柏灵, 刘正荣 2003 中国科学 (A辑) 33 325]
[4]	Rosenau P, Hyman J M C 1993 Phys. Rev. Lett. 70 564
[5]	Yan Z Y 2002 Chaos Soliton. Fract. 14 1151
[6]	Fan E G 2000 Phys. Lett. A 277 212
[7]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[8]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[9]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 40 137
[10]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. 40 143
[11]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[12]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[13]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[14]	Xie F D, Chen J, Lü Z S 2005 Commun. Theor. Phys. 43 585
[15]	Xie F D, Yuan Z T 2005 Commun. Theor. Phys. 43 39
[16]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 39 647
[17]	Lü Z S, Zhang H Q 2003 Commun. Theor. Phys. 39 405
[18]	Xie F D, Gao X S 2004 Commun. Theor. Phys. 41 353
[19]	Chen Y, Li B 2004 Commun. Theor. Phys. 41 1
[20]	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]
[21]	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]
[22]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆 2003 52 1569]
[23]	Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 504 (in Chinese) [曾昕, 张鸿庆 2005 54 504]
[24]	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]
[25]	Pan J T, Gong L X 2008 Chin. Phys. B 17 399
[26]	Jiao X Y, Wang J H, Zhang H Q 2005 Commun. Theor. Phys. 44 407
[27]	Liu Y P, Li Z B 2003 Chin. Phys. Lett. 20 317
[28]	Xu G Q, Li Z B 2003 Commun. Theor. Phys. 39 39
[29]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 6214 (in Chinese) [套格图桑, 斯仁道尔吉 2006 55 6214]
[30]	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]
[31]	Li Z L 2009 Chin. Phys. B 18 4074
[32]	Huang D J, Zhang H Q 2004 Acta Phys. Sin. 53 2434 (in Chinese) [黄定江, 张鸿庆 2004 53 2434]
[33]	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 2003 52 1827]
[34]	Wang Z, Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
[35]	Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565 (in Chinese) [李德生, 张鸿庆 2006 55 1565]
[36]	Yong X L, Zhang H Q 2005 Acta Phys. Sin. 54 2514 (in Chinese) [雍雪林, 张鸿庆 2005 54 2514]
[37]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[38]	Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[39]	Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[40]	Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[41]	Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
[42]	Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin. Phys. 15 2202
[43]	Li J B 2007 Sci. China A Math. 50 153
[44]	Li H M 2003 Commun. Theor. Phys. 39 395
[45]	Li H M 2005 Chin. Phys. 14 251
[46]	Taogetusang, Sirendaoerji 2006 Chin.Phys. 15 2809
[47]	Liu C S 2005 Chin. Phys. 14 1710
[48]	Zhu J M, Zheng C L, Ma Z Y 2004 Chin. Phys. 13 2008
[49]	Fu Z T, Liu S D, Liu S K 2003 Commun. Theor. Phys. 39 531
[50]	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]
[51]	Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 56 5585]
[52]	Taogetusang, Sirendaoerji 2008 Acta Phys. Sin. 57 1295 (in Chinese) [套格图桑, 斯仁道尔吉 2008 57 1295]
[53]	Sirendaoerji, Sun J 2003 Phys. Lett. A 309 387
[54]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑, 斯仁道尔吉 2006 55 3246]
[55]	Taogetusang, Sirendaoerji 2006 Chin. Phys. 15 1143
[56]	Taogetusang, Sirendaoerji 2007 Acta Phys. Sin. 56 627 (in Chinese) [套格图桑, 斯仁道尔吉 2007 56 627]
[57]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑, 斯仁道尔吉 2006 55 13]
[58]	Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999 (in Chinese) [毛杰健, 杨建荣 2005 54 4999]
[59]	Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. 39 27
[60]	Yu J, Ke Y Q, Zhang W J 2004 Commun. Theor. Phys. 40 493
[61]	Sirendaoerji, Sun J 2002 Phys. Lett. A 298 133
[62]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 2373 (in Chinese) [李德生, 张鸿庆 2006 52 2373]
[63]	Zhao C H, Sheng Z M 2004 Acta Phys. Sin. 53 1629 (in Chinese) [赵长海, 盛正卯 2004 53 1629]
[64]	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]
[65]	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]
[66]	Taogetusang, Sirendaoerji 2010 Acta Phys. Sin. 59 4413 (in Chinese) [套格图桑, 斯仁道尔吉 2010 59 4413]

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