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.
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