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We study the Cauchy problem for the Schr\"odinger-improved Boussinesq systemin a two dimensional domain. Under natural assumptions on the data withoutsmallness, we prove the existence and uniqueness of global strong solutions.Moreover, we consider the vanishing "improvement" limit of global solutions asthe coefficient of the linear term of the highest order in the equation of ionsound waves tends to zero. Under the same smallness assumption on the data asin the Zakharov case, solutions in the vanishing "improvement" limit are shownto satisfy the Zakharov system.

Schr\"odinger-improved Boussinesq system in two space dimensions