“…The solution of the nonlinear problem strongly depends on the initial waveshape. Various shapes of the periodic incident wave trains such as the sine wave [Kaistrenko et al, 1991;Madsen and Fuhrman, 2007], cnoidal wave [Synolakis, 1991] and nonlinear deformed periodic waves [Didenkulova et al, 2006[Didenkulova et al, , 2007 have been analyzed in the literature. The relevant analysis has been also performed for a variety of solitary waves and single pulses such as soliton [Pedersen and Gjevik, 1983;Synolakis, 1987;Kânoglu, 2004], sine pulse , Lorentz pulse [Pelinovsky and Mazova, 1992], Gaussian pulse [Carrier et al, 2003;Kânoglu and Synolakis, 2006], N waves [Tadepalli and Synolakis, 1994], and ''characterized tsunami waves'' [Tinti and Tonini, 2005].…”