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Article

General initial value problem for the nonlinear shallow water equations: runup of tsunamis on sloping beaches and bays

Physics Letters A. 2018. Vol. 382. No. 38. P. 2738-2743.
Pelinovsky E., Rybkin A., Nicolsky D., Raz A.

We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier–Greenspan transformation (Carrier and Greenspan (1957) [9]). We use a Taylor series approximation to deal with the difficulty associated with the initial conditions given on a curve in the transformed space. This extends earlier solutions to waves with near shore initial conditions, large initial velocities, and in more complex U-shaped bathymetries; and allows verification of tsunami wave inundation models in a more realistic 2-D setting