Infinite sequence new exact solutions of K(m,n) equation and B(m,n) equation

Bai Yu-Mei; Taogetusang; Han Yuan-Chun

doi:10.7498/aps.61.200205

Abstract

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:

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).

References

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[6]	Fan E G 2000 Phys. Lett. A 277 212
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[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
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[13]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
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[38]	Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
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[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
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[45]	Li H M 2005 Chin. Phys. 14 251
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[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]

Cited By

[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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Vol. 61, Issue 20 - 2012-10-20

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