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2003 A higher-order nonlinear Schrödinger equation with variable coefficients
X. Carvajal, F. Linares
Differential Integral Equations 16(9): 1111-1130 (2003).

Abstract

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.

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X. Carvajal. F. Linares. "A higher-order nonlinear Schrödinger equation with variable coefficients." Differential Integral Equations 16 (9) 1111 - 1130, 2003.

Information

Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1042.35073
MathSciNet: MR1989544

Subjects:
Primary: 35Q55
Secondary: 35B30

Rights: Copyright © 2003 Khayyam Publishing, Inc.

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Vol.16 • No. 9 • 2003
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