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The tsunami run-up problem is solved non-linearly under the most general initial conditions, that is, for realistic initial waveforms such as N-waves, as well as standard initial waveforms such as solitary waves, in the presence of initial velocity. An initial-boundary value problem governed by the non-linear shallow-water wave equations is solved analytically utilizing the classical separation of variables technique, which proved to be not only fast but also accurate analytical approach for this type of problems. The results provide important information on maximum tsunami run-up qualitatively. We observed that, although the calculated maximum run-ups increase significantly, going as high as double that of the zero-velocity case, initial waves having non-zero fluid velocity exhibit the same run-up behavior as waves without initial velocity, for all wave types considered in this study.

Maximum run-up behavior of tsunamis under non-zero initial velocity condition