A higher-order nonlinear Schrodinger equation with variable coefficients

X. Carvajal; F. Linares

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A higher-order nonlinear Schrodinger equation with variable coefficients

机译：变系数的高阶非线性薛定inger方程

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We study the initial value problem (IVP) associated to a higher-order nonlinear Schrodinger equation with variable coefficients. Under some regularity on its coefficients we establish local well-posedness for the IVP for data in H~s(R), s ≥ 1/4, improving previous results [22]. The main ingredient in our proof is an estimate of the maximal function associated to the linear solution similar to the sharp one obtained for linear solutions of the Schrodinger and Korteweg-de Vries equations.

机译：我们研究了与具有可变系数的高阶非线性Schrodinger方程相关的初始值问题（IVP）。在其系数有一定规律性的情况下，我们为H〜s（R）中s≥1/4的数据建立了IVP的局部适定性，从而改善了先前的结果[22]。我们证明中的主要成分是与线性解相关的最大函数的估计，类似于针对Schrodinger和Korteweg-de Vries方程的线性解所获得的尖锐函数。

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《Differential and integral equations》 |2003年第9期|共20页
作者
X. Carvajal; F. Linares;
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中图分类微分方程、积分方程;
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A higher-order nonlinear Schrodinger equation with variable coefficients

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