Asymptotic Behavior of a Shallow-Water Soliton Reflected at a Sloping Beach

  • N. Sugimoto
  • T. Kakutani
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


This paper deals with a long-time asymptotic behavior of a shallow water soliton reflected at a sloping beach. Based on the edge-layer theory, it is shown that the boundary-value problem for the Boussinesq equation under the “reduced” boundary condition is simplified to an “initial value” problem for the Korteweg-de Vries equation in the form of the spatial evolution of the reflected wave. Solving it numerically, the asymptotic behavior is demonstrated and compared with the one which evolves from the “initial value” obtained by solving the full nearshore behavior by the boundary element method.


Solitary Wave Incident Wave Boundary Element Method Surface Elevation Boussinesq Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sugimoto, N.; Kakutani, T.: Reflection of a shallow-water soli-ton. Part 1. Edge-layer theory for shallow-water waves. J. Fluid Mech. 146 (1984) 369–382.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Sugimoto, N.; Kusaka, Y.; Kakutani, T.: Reflection of a shallow-water soliton. Part 2. Numerical evaluation. J. Fluid Mech. 178 (1987) 99–117.MATHCrossRefGoogle Scholar
  3. 3.
    Miles, J. W.: Obliquely interacting solitary waves. J. Fluid Mech. 79 (1977) 157–169.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Pedersen, G.; Gjevik, B.: Run-up of solitary waves. J. Fluid Mech. 135 (1983) 283–299.MATHCrossRefGoogle Scholar
  5. 5.
    Zabusky, N. J.; Kruskal, M. D.: Interaction of “so litons” in a collisionless plasma and the recurrence of initial state. Phys. Rev. Letts. 15 (1965) 240–243.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • N. Sugimoto
    • 1
  • T. Kakutani
    • 1
  1. 1.Department of Mechanical Engineering Faculty of Engineering ScienceOsaka UniversityToyonaka, Osaka 560Japan

Personalised recommendations