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Exact solutions and invariants of motion for general types of regularized long wave equations

Author

Listed:
  • Hamdi, S.
  • Enright, W.H.
  • Schiesser, W.E
  • Gottlieb, J.J.

Abstract

New exact solitary wave solutions are derived for general types of the regularized long wave (RLW) equation and its simpler alternative, the generalized equal width wave (EW) equation, which are evolutionary partial differential equations for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. New exact solitary wave solutions are also derived for the generalized EW-Burgers equation, which models the propagation of nonlinear and dispersive waves with certain dissipative effects. The analytical solutions for these model equations are obtained for any order of the nonlinear terms and for any given value of the coefficients of the nonlinear, dispersive and dissipative terms. Analytical expressions for three invariants of motion for solitary wave solutions of the generalized EW equation are also devised.

Suggested Citation

  • Hamdi, S. & Enright, W.H. & Schiesser, W.E & Gottlieb, J.J., 2004. "Exact solutions and invariants of motion for general types of regularized long wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 65(4), pages 535-545.
    • Handle: RePEc:eee:matcom:v:65:y:2004:i:4:p:535-545
    DOI: 10.1016/j.matcom.2004.01.015
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    Cited by:

    1. Karakoç, S. Battal Gazi & Zeybek, Halil, 2016. "Solitary-wave solutions of the GRLW equation using septic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 159-171.
    2. Wang, Xiaofeng & Dai, Weizhong & Guo, Shuangbing, 2019. "A conservative linear difference scheme for the 2D regularized long-wave equation," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 55-70.

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