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New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation

Narenmandula Taogetusang

New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation

Narenmandula, Taogetusang
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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.
    • Funds:
    [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]

  • [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]

  • [1] Taogetusang, Bai Yu-Mei. New type infinite sequence exact solutions of the second KdV equation with variable coefficients. Acta Physica Sinica, 2012, 61(6): 060201. doi: 10.7498/aps.61.060201
    [2] Taogetusang, Sirendaoerji. A method for constructing exact solutions of nonlinear evolution equation with variable coefficients. Acta Physica Sinica, 2009, 58(4): 2121-2126. doi: 10.7498/aps.58.2121
    [3] Taogetusang, Yi Li-Na. New complexion two-soliton solutions to a kind of nonlinear coupled system. Acta Physica Sinica, 2014, 63(16): 160201. doi: 10.7498/aps.63.160201
    [4] Taogetusang, Bai Yu Mei. Riemann theta function and other several kinds of new solutions of nonlinear evolution equations. Acta Physica Sinica, 2013, 62(10): 100201. doi: 10.7498/aps.62.100201
    [5] Bai Yu-Mei, Taogetusang, Han Yuan-Chun. Infinite sequence new exact solutions of K(m,n) equation and B(m,n) equation. Acta Physica Sinica, 2012, 61(20): 200205. doi: 10.7498/aps.61.200205
    [6] Taogetusang. New infinite sequence exact solutions to the general lattice. Acta Physica Sinica, 2010, 59(10): 6712-6718. doi: 10.7498/aps.59.6712
    [7] Taogetusang, Sirendaoerji. New exact infinite sequence solutions to generalized Boussinesq equation. Acta Physica Sinica, 2010, 59(7): 4413-4419. doi: 10.7498/aps.59.4413
    [8] Taogetusang. New infinite sequences exact solutions to sine-Gordon-type equations. Acta Physica Sinica, 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
    [9] Liu Ping, Xu Heng-Rui, Yang Jian-Rong. The Boussinesq equation: Lax pair, Bäcklund transformation, symmetry group transformation and consistent Riccati expansion solvability. Acta Physica Sinica, 2020, 69(1): 010203. doi: 10.7498/aps.69.20191316
    [10] Taogetusang, Bai Yu-Mei. A method of constructing infinite sequence soliton-like solutions of nonlinear evolution equations. Acta Physica Sinica, 2012, 61(13): 130202. doi: 10.7498/aps.61.130202
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Publishing process
  • Received Date:  22 November 2010
  • Accepted Date:  16 December 2010
  • Published Online:  15 September 2011

New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation

  • 1. (1)College of Physics and Electronics, Inner Mongolia University for Nationalities, Tongliao 028043, China; (2)The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Abstract: 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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