On a Class of Boussinesq Equations for Shallow Water Waves Conference Paper uri icon


  • The Euler's equations describing the dynamics of capillary-gravity water waves in two-dimensions are considered in the limits of small-amplitude and long-wavelength under appropriate boundary conditions. Using a double-series perturbation analysis, a general Boussinesq type of equation is derived involving the small-amplitude and long-wavelength parameters. A recently introduced sixth-order Boussinesq equation by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159-207] is recovered from this equation in the 1/3 Bond number limit (from below) when the above parameters bear a certain relationship as they approach zero. © Springer-Verlag Berlin Heidelberg 2003.

author list (cited authors)

  • Daripa, P., & Dash, R. K.

citation count

  • 0

editor list (cited editors)

  • Kumar, V., Gavrilova, M. L., Tan, C., & L'Ecuyer, P.

publication date

  • June 2003