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Progressive Long Waves on a Slope (A New Solution to the Euler Equation?)

In: Computer Algebra in Scientific Computing CASC 2001

Author

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  • Alexander Shermenev

    (Russian Academy of Science, Wave Research Center)

Abstract

Computer algebra system is used for deriving and studying high-order Boussinesq-type equations for long periodic nonlinear waves climbing a sloping beach. Potential and surface elevation for wave motion are expanded in Fourier series up to the fourth harmonic inclusively. Coefficients of these series are explicitly presented as polynomials in Bessel functions. One may speculate that the obtained expressions are the first terms of the expanded exact solution to the Euler equation for surface waves.

Suggested Citation

  • Alexander Shermenev, 2001. "Progressive Long Waves on a Slope (A New Solution to the Euler Equation?)," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC 2001, pages 477-489, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56666-0_36
    DOI: 10.1007/978-3-642-56666-0_36
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