Wave Wall for waves on the surface of a heavy liquid

Asymptotic analysis of surface water waves is made. Gradient of the ocean depth is assumed small. The ansatz for the asymptotic expansion in this small parameter is suggested. The goal is to construct full asymptotic expansion for the solution localized near moving line on the liquid surface. The approach is based on space-time ray method. Eiconal and amplitudes are found in the forms of formal power series. Chains of recurrent equations for its terms are derived. Their solvability is proved. The first term is obtained in explicit form.