Differential and Integral Equations

A higher-order nonlinear Schrödinger equation with variable coefficients

X. Carvajal and F. Linares

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We study the initial value problem (IVP) associated to a higher-order nonlinear Schrödinger equation with variable coefficients. Under some regularity on its coefficients we establish local well-posedness for the IVP for data in $H^s(\mathbb R)$, $s\ge1/4$, 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 Schrödinger and Korteweg-de Vries equations.

Article information

Differential Integral Equations, Volume 16, Number 9 (2003), 1111-1130.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]


Carvajal, X.; Linares, F. A higher-order nonlinear Schrödinger equation with variable coefficients. Differential Integral Equations 16 (2003), no. 9, 1111--1130. https://projecteuclid.org/euclid.die/1356060560

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