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Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations

Author

Listed:
  • Shi Jing
  • Yan Xin-li

Abstract

The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.

Suggested Citation

  • Shi Jing & Yan Xin-li, 2014. "Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:487571
    DOI: 10.1155/2014/487571
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    References listed on IDEAS

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    1. Shen, Jianwei & Xu, Wei & Li, Wei, 2006. "Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 413-425.
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