New Analytical Solution for Nonlinear Shallow Water-Wave Equations


AYDIN B., KANOĞLU U.

PURE AND APPLIED GEOPHYSICS, vol.174, no.8, pp.3209-3218, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 174 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1007/s00024-017-1508-z
  • Title of Journal : PURE AND APPLIED GEOPHYSICS
  • Page Numbers: pp.3209-3218

Abstract

We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-averaged velocity, compare with existing solutions, and observe perfect agreement with substantially less computational effort.