  We study the Cauchy problem for the Schr\"odinger-improved Boussinesq system
in a two dimensional domain. Under natural assumptions on the data without
smallness, we prove the existence and uniqueness of global strong solutions.
Moreover, we consider the vanishing "improvement" limit of global solutions as
the coefficient of the linear term of the highest order in the equation of ion
sound waves tends to zero. Under the same smallness assumption on the data as
in the Zakharov case, solutions in the vanishing "improvement" limit are shown
to satisfy the Zakharov system.
