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In the paper, to construct new infinite sequence exact solutions of nonlinear evolution equations, several kinds of new solutions of the second kind of elliptic equation Bäcklund transformation are proposed. The KdV equation containing variable coefficients and forcible term, combined with (2+1)-dimensional and (3+1)-dimensional Zakharov-Kuznetsov equation with variable coefficients is taken as example to construct new infinite sequence exact solutions of these equations with the help of symbolic computation system Mathematica, which include infinite sequence compact soliton solutions of Jacobi elliptic function and triangular function, and infinite sequence peak soliton solutions.
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Keywords:
- the second kind of elliptic equation /
- Bä /
- cklund transformation /
- nonlinear evolution equation with variable coefficients /
- new infinite sequence exact solution
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[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
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[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
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[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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[29] Yin J L, Tian L X 2007 ActaMath.Phys.27A 027(in Chinese)[殷久利、田立新 2007 数学 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 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 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 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 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 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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