带强迫项变系数组合KdV方程的无穷序列复合型类孤子新解

伊丽娜; 套格图桑

doi:10.7498/aps.63.030201

摘要

为了获得变系数非线性发展方程的无穷序列复合型新解，研究了[G（）]/[G（）] 展开法. 通过引入一种函数变换，把常系数二阶齐次线性常微分方程的求解问题转化为一元二次方程和Riccati方程的求解问题. 在此基础上，利用Riccati方程解的非线性叠加公式，获得了常系数二阶齐次线性常微分方程的无穷序列复合型新解. 借助这些复合型新解与符号计算系统Mathematica，构造了带强迫项变系数组合KdV方程的无穷序列复合型类孤子新精确解.

关键词:

Abstract

The [G()]/[G()] expansion method is extensively studied to search for new infinite sequence of complex solutions to nonlinear evolution equations with variable coefficients. According to a function transformation, the solving of homogeneous linear ordinary differential equation with constant coefficients of second order can be changed into the solving of a one-unknown quadratic equation and the Riccati equation. Based on this, new infinite sequence complex solutions of homogeneous linear ordinary differential equation with constant coefficients of second order are obtained by the nonlinear superposition formula of the solutions to Riccati equation. By means of the new complex solutions, new infinite sequence complex soliton-like exact solutions to the combined KdV equation with variable coefficients and forced term are constructed with the help of symbolic computation system Mathematica.

Keywords:

作者及机构信息

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：11361040）、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.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Funds: Project supported by the Natural Natural Science Foundation of China(Grant No. 11361040), 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]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[2]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[3]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[4]	L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[5]	Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[6]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[7]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[8]	Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[9]	Yan Z Y, Zhang H Q 1999 Acta. Phys. Sin. 48 1957 (in Chinese) [闫振亚, 张鸿庆 1999 物理学报 48 1957]
[10]	Zhang J F, Chen Y F 2001 Acta. Phys. Sin. 50 1648 (in Chinese) [张解放, 陈芳跃 2001 物理学报 50 1648]
[11]	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]
[12]	Liu C S 2005 Acta. Phys. Sin. 54 4506 (in Chinese) [刘成仕 2005 物理学报 54 4506]
[13]	Liu S K, Fu Z T, Liu S D 2002 Acta. Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达 2002 物理学报 51 1923]
[14]	Lu D C, Hong B J, Tian L X 2006 Acta. Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[15]	Mustafa Inca, Esma Ulutas, Anjan Biswasc 2013 Chin. Phys. B 22 060204
[16]	Sirendaoreji, Sun J 2003 Phys. Lett. A309 387
[17]	Khaled A. Gepreel, Saleh Omran 2012 Chin. Phys. B 21 110204
[18]	Zhang S 2007 Phys. Lett. A 368 470
[19]	Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[20]	Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[21]	Wang M L 1995 Phys. Lett. A199 169
[22]	Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A216 67
[23]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[24]	Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing, China) 39 27
[25]	Liu S K, Chen H, Fu Z T Liu S D 2003 Acta. Phys. Sin. 52 1842 (in Chinese) [刘式适, 陈华, 付遵涛, 刘式达 2003 物理学报 52 1842]
[26]	Ma Y L, Li B Q, Sun J Z 2009 Acta. Phys. Sin. 58 7403 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 物理学报 58 7403]
[27]	Li B Q, Ma Y L, Xu M P 2010 Acta. Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰, 徐美萍 2010 物理学报 59 1409]
[28]	Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373(in Chinese) [李帮庆, 马玉兰 2009 物理学报 58 4373]
[29]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[30]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[31]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303

施引文献

[1]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[2]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[3]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[4]	L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[5]	Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[6]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[7]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[8]	Ma S H, Fang J P, Zheng C L 2008 Chin. Phys. B 17 2767
[9]	Yan Z Y, Zhang H Q 1999 Acta. Phys. Sin. 48 1957 (in Chinese) [闫振亚, 张鸿庆 1999 物理学报 48 1957]
[10]	Zhang J F, Chen Y F 2001 Acta. Phys. Sin. 50 1648 (in Chinese) [张解放, 陈芳跃 2001 物理学报 50 1648]
[11]	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]
[12]	Liu C S 2005 Acta. Phys. Sin. 54 4506 (in Chinese) [刘成仕 2005 物理学报 54 4506]
[13]	Liu S K, Fu Z T, Liu S D 2002 Acta. Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达 2002 物理学报 51 1923]
[14]	Lu D C, Hong B J, Tian L X 2006 Acta. Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[15]	Mustafa Inca, Esma Ulutas, Anjan Biswasc 2013 Chin. Phys. B 22 060204
[16]	Sirendaoreji, Sun J 2003 Phys. Lett. A309 387
[17]	Khaled A. Gepreel, Saleh Omran 2012 Chin. Phys. B 21 110204
[18]	Zhang S 2007 Phys. Lett. A 368 470
[19]	Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[20]	Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[21]	Wang M L 1995 Phys. Lett. A199 169
[22]	Wang M L, Zhou Y B, Li Z B 1996 Phys. Lett. A216 67
[23]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[24]	Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing, China) 39 27
[25]	Liu S K, Chen H, Fu Z T Liu S D 2003 Acta. Phys. Sin. 52 1842 (in Chinese) [刘式适, 陈华, 付遵涛, 刘式达 2003 物理学报 52 1842]
[26]	Ma Y L, Li B Q, Sun J Z 2009 Acta. Phys. Sin. 58 7403 (in Chinese) [马玉兰, 李帮庆, 孙践知 2009 物理学报 58 7403]
[27]	Li B Q, Ma Y L, Xu M P 2010 Acta. Phys. Sin. 59 1409 (in Chinese) [李帮庆, 马玉兰, 徐美萍 2010 物理学报 59 1409]
[28]	Li B Q, Ma Y L 2009 Acta. Phys. Sin. 58 4373(in Chinese) [李帮庆, 马玉兰 2009 物理学报 58 4373]
[29]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A372 417
[30]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
[31]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303

[1]	套格图桑, 伊丽娜. 一类非线性发展方程的复合型双孤子新解. 物理学报, 2015, 64(2): 020201. doi: 10.7498/aps.64.020201
[2]	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
[3]	尹君毅. (2+1)维改进的Zakharov-Kuznetsov方程的无穷序列复合型类孤子新解. 物理学报, 2014, 63(23): 230202. doi: 10.7498/aps.63.230202
[4]	套格图桑, 伊丽娜. 一类非线性耦合系统的复合型双孤子新解. 物理学报, 2014, 63(16): 160201. doi: 10.7498/aps.63.160201
[5]	万晖. 带源项的变系数非线性反应扩散方程的精确解. 物理学报, 2013, 62(9): 090203. doi: 10.7498/aps.62.090203
[6]	尹君毅. 扩展的(G/G)展开法和Zakharov方程组的新精确解. 物理学报, 2013, 62(20): 200202. doi: 10.7498/aps.62.200202
[7]	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
[8]	套格图桑. 构造非线性发展方程的无穷序列复合型类孤子新解. 物理学报, 2013, 62(7): 070202. doi: 10.7498/aps.62.070202
[9]	庞晶, 靳玲花, 赵强. 变系数非线性发展方程的G'/G展开解. 物理学报, 2012, 61(14): 140201. doi: 10.7498/aps.61.140201
[10]	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
[11]	李帮庆, 马玉兰, 徐美萍. （G'/G）展开法与高维非线性物理方程的新分形结构. 物理学报, 2010, 59(3): 1409-1415. doi: 10.7498/aps.59.1409
[12]	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
[13]	李帮庆, 马玉兰. (G′/G)展开法和(2+1)维非对称Nizhnik-Novikov-Veselov系统的新精确解. 物理学报, 2009, 58(7): 4373-4378. doi: 10.7498/aps.58.4373
[14]	马玉兰, 李帮庆, 孙践知. (G′/G)展开法在高维非线性物理方程中的新应用. 物理学报, 2009, 58(11): 7402-7409. doi: 10.7498/aps.58.7402
[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]	卢殿臣, 洪宝剑, 田立新. 带强迫项变系数组合KdV方程的显式精确解. 物理学报, 2006, 55(11): 5617-5622. doi: 10.7498/aps.55.5617
[17]	来娴静, 张解放. 两类2+1维非线性波动方程的线性叠加解. 物理学报, 2004, 53(12): 4065-4069. doi: 10.7498/aps.53.4065
[18]	刘式适, 付遵涛, 刘式达, 赵强. 变系数非线性方程的Jacobi椭圆函数展开解. 物理学报, 2002, 51(9): 1923-1926. doi: 10.7498/aps.51.1923
[19]	刘式适, 傅遵涛, 刘式达, 赵强. Jacobi椭圆函数展开法及其在求解非线性波动方程中的应用. 物理学报, 2001, 50(11): 2068-2073. doi: 10.7498/aps.50.2068
[20]	张解放, 陈芳跃. 截断展开方法和广义变系数KdV方程新的精确类孤子解. 物理学报, 2001, 50(9): 1648-1650. doi: 10.7498/aps.50.1648

计量

文章访问数: 5984
PDF下载量: 665
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