Invariant solutions of variable coefficients generalized Gardner equation
详细信息    查看全文
  • 作者:Rajeev Kumar ; R. K. Gupta ; S. S. Bhatia
  • 关键词:Lie classical method ; Gardner equation ; Traveling wave solutions
  • 刊名:Nonlinear Dynamics
  • 出版年:2016
  • 出版时间:March 2016
  • 年:2016
  • 卷:83
  • 期:4
  • 页码:2103-2111
  • 全文大小:1,800 KB
  • 参考文献:1.Lamb, K.G., Stastna, M.: Large fully nonlinear internal solitary waves: the effect of back-ground current. Phys. Fluids 14, 2897–2999 (2002)
    2.Wazwaz, A.M.: New solitons and kink solutions for the Gardner equation. Commun. Nonlinear Sci. Numer. Simul. 12, 1395–1404 (2007)
    3.Demina, M.V., Kudryashov, N.A., Sinel’shchikov, D.I.: The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves. Comput. Math. Math. Phys. 48, 2182–2193 (2008)CrossRef MathSciNet
    4.Zhang, J.: New solitary wave solution of the combined KdV and mKdV equation. Int. J. Theor. Phys. 37, 1541–1546 (1998)CrossRef MATH
    5.Singh, K., Gupta, R.K.: Lie symmetries and exact solutions of a new generalized Hirota–Satsuma coupled KdV system with variable coefficients. Int. J. Eng. Sci. 44, 241–255 (2006)CrossRef MathSciNet MATH
    6.Kumar, S., Singh, K., Gupta, R.K.: Painlevé analysis, Lie symmetries and exact solutions for (2+1)-dimensional variable coefficients Broer–Kaup equations. Commun. Nonlinear Sci. Numer. Simul. 17, 1529–1541 (2012)CrossRef MathSciNet MATH
    7.Gupta, R.K., Bansal, A.: Similarity reductions and exact solutions of generalized Bretherton equation with time-dependent coefficients. Nonlinear Dyn. 71, 1–12 (2013)CrossRef MathSciNet MATH
    8.Kumar, R., Gupta, R.K., Bhatia, S.S.: Lie symmetry analysis and exact solutions for a variable coefficients generalised Kuramoto–Sivashinsky equation. Rom. Rep. Phys. 66, 923–928 (2014)
    9.Bluman, G.W., Cole, J.D.: Similarity Methods for Differential Equations. Springer, New York (1974)CrossRef MATH
    10.Kumar, V., Gupta, R.K., Jiwari, R.: Painlevé analysis, Lie symmetries and exact solution for variable coefficients Benjamin–Bona–Mahony–Burger(BBMB) equation. Commun. Theor. Phys. 60, 175–182 (2013)CrossRef MathSciNet MATH
    11.Malik, A., Chand, F., Kumar, H., Misra, S.C.: Exact solutions of some physical models using the \(\frac{G^{\prime }}{G}\) -expansion method. Pramana J. Phys. 78, 513–529 (2012)CrossRef
    12.Wang, M.L., Li, X.Z., Zhang, J.L.: The \(\frac{G^{\prime }}{G}\) -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372, 417–423 (2008)CrossRef MathSciNet MATH
    13.Zhang, H.: New application of the \(\frac{G^{\prime }}{G}\) -expansion method. Commun. Nonlinear Sci. Numer. Simul. 14, 3220–3225 (2009)CrossRef MATH
    14.Zayed, E.M.E.: Exact solutions of nonlinear partial differential equations in mathematical physics using the \(\frac{G^{\prime }}{G}\) -expansion method. Adv. Theor. Appl. Mech. 4, 91–100 (2011)MathSciNet MATH
    15.Zhang, L., Chen, L., Huo, X.: Peakons and periodic cusp wave solutions in a generalized Camassa–Holm equation. Chaos Solitons Fractals 30, 1238–1249 (2006)CrossRef MathSciNet MATH
    16.Elwakil, S.A., El-Hanbaly, A.M., El-Shewy, E.K., El-Kamash, I.S.: Symmetries and exact solutions of KP equation with an arbitrary nonlinear term. J. Theor. Appl. Phys. 8, 93–102 (2014)CrossRef
  • 作者单位:Rajeev Kumar (1)
    R. K. Gupta (2)
    S. S. Bhatia (2)

    1. Department of Mathematics, Maharishi Markandeshwar Univesity, Mullana, Ambala, 131001, Haryana, India
    2. School of Mathematics and Computer Applications, Thapar University, Patiala, 147004, Punjab, India
  • 刊物类别:Engineering
  • 刊物主题:Vibration, Dynamical Systems and Control
    Mechanics
    Mechanical Engineering
    Automotive and Aerospace Engineering and Traffic
  • 出版者:Springer Netherlands
  • ISSN:1573-269X
文摘
The similarity reduction and exact solutions of variable coefficients generalized Gardner equation are obtained by finding the symmetries using Lie classical method. Also, the bifurcation and the phase portrait of generalized Gardner equation have been presented. Keywords Lie classical method Gardner equation Traveling wave solutions

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700