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

[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 物理学报 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 物理学报 57 11]
[22]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆 2003 物理学报 52 1569]
[23]	Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 504 (in Chinese) [曾昕, 张鸿庆 2005 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 55 1565]
[36]	Yong X L, Zhang H Q 2005 Acta Phys. Sin. 54 2514 (in Chinese) [雍雪林, 张鸿庆 2005 物理学报 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 物理学报 57 3312]
[51]	Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 物理学报 56 5585]
[52]	Taogetusang, Sirendaoerji 2008 Acta Phys. Sin. 57 1295 (in Chinese) [套格图桑, 斯仁道尔吉 2008 物理学报 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 物理学报 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 物理学报 56 627]
[57]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑, 斯仁道尔吉 2006 物理学报 55 13]
[58]	Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999 (in Chinese) [毛杰健, 杨建荣 2005 物理学报 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 物理学报 52 2373]
[63]	Zhao C H, Sheng Z M 2004 Acta Phys. Sin. 53 1629 (in Chinese) [赵长海, 盛正卯 2004 物理学报 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 物理学报 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 物理学报 59 4413]

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 物理学报 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 物理学报 57 11]
[22]	Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆 2003 物理学报 52 1569]
[23]	Zeng X, Zhang H Q 2005 Acta Phys. Sin. 54 504 (in Chinese) [曾昕, 张鸿庆 2005 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 55 1565]
[36]	Yong X L, Zhang H Q 2005 Acta Phys. Sin. 54 2514 (in Chinese) [雍雪林, 张鸿庆 2005 物理学报 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 物理学报 57 3312]
[51]	Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 物理学报 56 5585]
[52]	Taogetusang, Sirendaoerji 2008 Acta Phys. Sin. 57 1295 (in Chinese) [套格图桑, 斯仁道尔吉 2008 物理学报 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 物理学报 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 物理学报 56 627]
[57]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑, 斯仁道尔吉 2006 物理学报 55 13]
[58]	Mao J J, Yang J R 2005 Acta Phys. Sin. 54 4999 (in Chinese) [毛杰健, 杨建荣 2005 物理学报 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 物理学报 52 2373]
[63]	Zhao C H, Sheng Z M 2004 Acta Phys. Sin. 53 1629 (in Chinese) [赵长海, 盛正卯 2004 物理学报 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 物理学报 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 物理学报 59 4413]

[1]	套格图桑, 伊丽娜. Camassa-Holm-r方程的无穷序列类孤子新解. 物理学报, 2014, 63(12): 120201. doi: 10.7498/aps.63.120201
[2]	王光辉, 王林雪, 王灯山, 刘丛波, 石玉仁. K（m,n,p）方程多-Compacton相互作用的数值研究. 物理学报, 2014, 63(18): 180206. doi: 10.7498/aps.63.180206
[3]	套格图桑. (2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解. 物理学报, 2013, 62(21): 210201. doi: 10.7498/aps.62.210201
[4]	徐兰兰, 陈怀堂. 变系数(2+1)维Nizhnik-Novikov-Vesselov方程的三孤子新解. 物理学报, 2013, 62(9): 090204. doi: 10.7498/aps.62.090204
[5]	套格图桑, 白玉梅. 构造非线性发展方程无穷序列类孤子精确解的一种方法. 物理学报, 2012, 61(13): 130202. doi: 10.7498/aps.61.130202
[6]	套格图桑, 白玉梅. 第二类变系数KdV方程的新类型无穷序列精确解. 物理学报, 2012, 61(6): 060201. doi: 10.7498/aps.61.060201
[7]	套格图桑, 白玉梅. Nizhnik-Novikov-Vesselov方程的无穷序列类孤子精确解. 物理学报, 2012, 61(11): 110203. doi: 10.7498/aps.61.110203
[8]	套格图桑. Degasperis-Procesi 方程的无穷序列尖峰孤立波解. 物理学报, 2011, 60(7): 070204. doi: 10.7498/aps.60.070204
[9]	套格图桑, 那仁满都拉. 第二种椭圆方程构造变系数非线性发展方程的无穷序列新精确解. 物理学报, 2011, 60(9): 090201. doi: 10.7498/aps.60.090201
[10]	套格图桑. 几种辅助方程与非线性发展方程的无穷序列精确解. 物理学报, 2011, 60(5): 050201. doi: 10.7498/aps.60.050201
[11]	套格图桑. 构造非线性发展方程无穷序列复合型精确解的一种方法. 物理学报, 2011, 60(1): 010202. doi: 10.7498/aps.60.010202
[12]	套格图桑. sine-Gordon型方程的无穷序列新精确解. 物理学报, 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
[13]	套格图桑. 一般格子方程新的无穷序列精确解. 物理学报, 2010, 59(10): 6712-6718. doi: 10.7498/aps.59.6712
[14]	套格图桑, 斯仁道尔吉. 广义Boussinesq方程的无穷序列新精确解. 物理学报, 2010, 59(7): 4413-4419. doi: 10.7498/aps.59.4413
[15]	套格图桑, 斯仁道尔吉. 辅助方程构造带强迫项变系数组合KdV方程的精确解. 物理学报, 2008, 57(3): 1295-1300. doi: 10.7498/aps.57.1295
[16]	套格图桑, 斯仁道尔吉. 辅助方程构造(2+1)维Hybrid-Lattice系统和离散的mKdV方程的精确解. 物理学报, 2007, 56(2): 627-636. doi: 10.7498/aps.56.627
[17]	刘成仕. 用试探方程法求变系数非线性发展方程的精确解. 物理学报, 2005, 54(10): 4506-4510. doi: 10.7498/aps.54.4506
[18]	那仁满都拉, 乌恩宝音, 王克协. 具5次强非线性项的波方程新的孤波解. 物理学报, 2004, 53(1): 11-14. doi: 10.7498/aps.53.11
[19]	王烈衍. K(m,n)方程的对称性约化. 物理学报, 2000, 49(2): 181-185. doi: 10.7498/aps.49.181
[20]	鲍诚光. N体散射——(Ⅱ)非耦合积分方程. 物理学报, 1975, 24(6): 389-395. doi: 10.7498/aps.24.389

计量

文章访问数: 7359
PDF下载量: 591
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板