We study the Cauchy problem for the Schrödinger-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.
We study the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimentional 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 solusions 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.
We study the vanishing dispersion limit of strong solutions to the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimensional domain. We show an explicit representation of limiting profile in terms of the initial data. Moreover, the first approximation is also represented as a pair of solutions of a linear system with coefficients and forcing term given by the limiting profile.
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