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Crank-Nicolson – Differential quadrature algorithms for the Kawahara equation

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  • Korkmaz, Alper
  • Dağ, İdris

Abstract

The Kawahara equation is solved numerically using both Lagrange interpolation polynomials based differential quadrature method and cosine expansion based differential quadrature method. The travelling single solitary wave simulation is pictured. Maximum and discrete mean square error norms, lowest three conserved quantities are computed. Height, peak position and velocity of single solitary wave at various times are also computed for both methods. Breakup of an arbitrary single solitary wave into solitons and oscillatory shock wave generation from single solitary wave are studied.

Suggested Citation

  • Korkmaz, Alper & Dağ, İdris, 2009. "Crank-Nicolson – Differential quadrature algorithms for the Kawahara equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 65-73.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:65-73
    DOI: 10.1016/j.chaos.2008.10.033
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    References listed on IDEAS

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    1. Yusufoğlu, E. & Bekir, A. & Alp, M., 2008. "Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine–Cosine method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1193-1197.
    2. Ilison, O. & Salupere, A., 2005. "Propagation of sech2-type solitary waves in higher-order KdV-type systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 453-465.
    3. Zhang, Yi & Chen, Deng-yuan & Li, Zhi-bin, 2006. "A direct method for deriving a multisoliton solution to the fifth order KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1188-1193.
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