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Solitary wave solutions of the compound Burgers–Korteweg–de Vries equation

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  • Feng, Zhaosheng
  • Chen, Goong

Abstract

In this paper, the compound Burgers–Korteweg–de Vries equation is studied by the first integral method, which is based on ring theory in commutative algebra. Several new kink-profile waves and periodic waves are established. The applications of these results to other nonlinear wave equations such as the modified Burgers–KdV equation and the compound KdV equation are discussed. The stability and bifurcations of the kink-profile waves are also indicated.

Suggested Citation

  • Feng, Zhaosheng & Chen, Goong, 2005. "Solitary wave solutions of the compound Burgers–Korteweg–de Vries equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 419-435.
    • Handle: RePEc:eee:phsmap:v:352:y:2005:i:2:p:419-435
    DOI: 10.1016/j.physa.2004.12.061
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    Cited by:

    1. David, Claire & Sagaut, Pierre, 2009. "Spurious solitons and structural stability of finite-difference schemes for non-linear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 655-660.
    2. David, Claire & Sagaut, Pierre, 2009. "Structural stability of finite dispersion-relation preserving schemes," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2193-2199.
    3. David, Claire & Fernando, Rasika & Feng, Zhaosheng, 2007. "On solitary wave solutions of the compound Burgers–Korteweg–de Vries equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 44-50.
    4. David, Claire & Sagaut, Pierre, 2016. "Structural stability of Lattice Boltzmann schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 1-8.

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