  We consider the initial value problem to the Isobe-Kakinuma model for water
waves and the structure of the model. The Isobe-Kakinuma model is the
Euler-Lagrange equations for an approximate Lagrangian which is derived from
Luke's Lagrangian for water waves by approximating the velocity potential in
the Lagrangian. The Isobe-Kakinuma model is a system of second order partial
differential equations and is classified into a system of nonlinear dispersive
equations. Since the hypersurface $t=0$ is characteristic for the
Isobe-Kakinuma model, the initial data have to be restricted in an infinite
dimensional manifold for the existence of the solution. Under this necessary
condition and a sign condition, which corresponds to a generalized
Rayleigh-Taylor sign condition for water waves, on the initial data, we show
that the initial value problem is solvable locally in time in Sobolev spaces.
We also discuss the linear dispersion relation to the model.
