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本文为了获得非线性发展方程的无穷序列新精确解,进一步研究获得了第二种椭圆方程的几类新型解和Bäcklund变换.在此基础上,借助符号计算系统Mathematica,用带强迫项变系数组合KdV方程、(2+1)维和(3+1)维变系数Zakharov-Kuznetsov 方程为应用实例,构造了无穷序列新精确解.这里包括无穷序列Jacobi 椭圆函数光滑孤立子解、无穷序列Jacobi椭圆函数紧孤立子解、无穷序列三角函数紧孤立子解和无穷序列尖峰孤立子解.
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关键词:
- 第二种椭圆方程 /
- Bä /
- cklund 变换 /
- 变系数非线性发展方程 /
- 无穷序列新精确解
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[6] Rosenau P,Hyman, Compactons J M 1993 Phys. Rev. Lett.70 564
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[12] Sirendaoreji,Sun J 2003 Phys. Lett. A 309 169
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[22] Pan Z H, Ma S H, Fang J P 2010 Chin.Phys. B 19 100301-1
[23] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 647
[24] Lü Z S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 39 405
[25] Xie F D, Gao X S 2004 Commun.Theor.Phys. (Beijing) 41 353
[26] Chen Y, Fan E G 2007 Chin.Phys.16 6
[27] 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]
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[30] Alber M S,Camassa R 1994 Lett.Math.Phys. 32 137
[31] Clarkson P A,Mansfield E L,Priestley T J 1997 Math.Comput.Modelling 25 195
[32] Xin Z P,Zhang P 2000 Comm.Pure.Appl.Math.53 1411
[33] Michael Fisher,Jeremy Schiff 1999 Phys.Lett. A 259 371
[34] Adrian Constantin,Waner A Atrauss 2000 Comm.Pure.Appl.Math.53 603
[35] Tian L X, Xu G,Liu Z R 2002 Applied.Math.Mech.23 497(in Chinese)[田立新、许 刚、刘曾荣 2002 应用数学和力学 23 497]
[36] Taogetusang, Sirendaoerji 2010 ActaPhys.Sin. 594413(in Chinese)[套格图桑、斯仁道尔吉 2010 物理学报 59 4413]
[37] Lu D C, Hong B J, Tian L X 2006 ActaPhys.Sin.55 5617(in Chinese)[卢殿臣、烘宝剑、田立新 2006 物理学报 55 5617]
[38] Taogetusang, Sirendaoerji 2010 Chin.J.quantum.Electronics 27 6(in Chinese)[套格图桑、斯仁道尔吉 2010 量子电子学报 27 6]
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[1] Russell J S 1844 Reports on waves, Edinburgh: Proc. Royal. Soc. 311
[2] Korteweg D J, Vries G 1895 Phil.Mag.39 422
[3] Zabusky N, Kruskal M D 1965 Phys.Rev.Lett.15 240
[4] Camassa R,Holm D D 1993 Phys. Rev. Lett.71 1661
[5] Boyd J P 1997 Appl.Math.Comput. 81173
[6] Rosenau P,Hyman, Compactons J M 1993 Phys. Rev. Lett.70 564
[7] Yan Z Y 2002 Chaos,Solitons and Fractals 14 1151
[8] Wang M L 1995 Phys.Lett. A 199 279
[9] Parkes E J,Duffy B R 1996Comp.Phys.Commun. 98 288
[10] Parkes E J,Duffy B D 1997 Phys.Lett. A 229 217
[11] Fan E G 2000 Phys.Lett. A 277 212
[12] Sirendaoreji,Sun J 2003 Phys. Lett. A 309 169
[13] Li D S, Zhabg H Q 2004 Chin, Phys. 131377
[14] Chen Y, Li B, Zhang H Q 2003 Chin.Phys.12 940
[15] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin.Phys.12 1
[16] Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 137
[17] Li D S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 143
[18] Li D S, Zhang H Q 2004 Chin.Phys.13 984
[19] Li D S, Zhang H Q 2004 Chin.Phys.13 1377
[20] Chen H T, Zhang H Q 2004 Commun.Theor.Phys.(Beijing) 42 497
[21] Xie F D, Chen J, Lü Z S 2005 Commun.Theor.Phys.(Beijing) 43 585
[22] Pan Z H, Ma S H, Fang J P 2010 Chin.Phys. B 19 100301-1
[23] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 647
[24] Lü Z S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 39 405
[25] Xie F D, Gao X S 2004 Commun.Theor.Phys. (Beijing) 41 353
[26] Chen Y, Fan E G 2007 Chin.Phys.16 6
[27] 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]
[28] Guo B L, Liu Z R 2003 China Science. Sin. A33 325 (in Chinese)[郭柏灵、刘正荣 2003 中国科学 (A辑) 33 325]
[29] Yin J L, Tian L X 2007 ActaMath.Phys.27A 027(in Chinese)[殷久利、田立新 2007 数学物理学报 27A 027]
[30] Alber M S,Camassa R 1994 Lett.Math.Phys. 32 137
[31] Clarkson P A,Mansfield E L,Priestley T J 1997 Math.Comput.Modelling 25 195
[32] Xin Z P,Zhang P 2000 Comm.Pure.Appl.Math.53 1411
[33] Michael Fisher,Jeremy Schiff 1999 Phys.Lett. A 259 371
[34] Adrian Constantin,Waner A Atrauss 2000 Comm.Pure.Appl.Math.53 603
[35] Tian L X, Xu G,Liu Z R 2002 Applied.Math.Mech.23 497(in Chinese)[田立新、许 刚、刘曾荣 2002 应用数学和力学 23 497]
[36] Taogetusang, Sirendaoerji 2010 ActaPhys.Sin. 594413(in Chinese)[套格图桑、斯仁道尔吉 2010 物理学报 59 4413]
[37] Lu D C, Hong B J, Tian L X 2006 ActaPhys.Sin.55 5617(in Chinese)[卢殿臣、烘宝剑、田立新 2006 物理学报 55 5617]
[38] Taogetusang, Sirendaoerji 2010 Chin.J.quantum.Electronics 27 6(in Chinese)[套格图桑、斯仁道尔吉 2010 量子电子学报 27 6]
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