二维空间中具有积分型非线性Schrodinger方程组的初值问题

On the Initial Value Problem of the Schrodinger Equation with a Nonlinear Integral Term in Two Dimensional Space

具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程是在研究非线性Ｌａｎｇｍｕｉｒ波时考虑到离子惯性作用而导出的．本文讨论了二维空间中具有积分型非线性ｓｃｈｒｏｄｉｎｇｅｒ方程组的初值问题，用积分估计方法证明了整体解的存在唯一性．

The Schrodinger equation with a nonlinear integral term is deduced from the study of the nonlinear Langmuir wave of plasma with the influence of ion inertia.In this paper,the initial value problem of the Schrodinger equations with a nonlinear integral term in two dimensional space is considered,and the existence and the uniqueness of the global solution are proved with the integral estimate method.