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1997 On the generalized Korteweg-de Vries-type equations
Gigliola Staffilani
Differential Integral Equations 10(4): 777-796 (1997).

Abstract

We show well-posedness results for the generalized Korteweg-de Vries equation with nonlinear term $F(u)\partial_xu$. We assume $F(u)$ is a $C^4$ function and $F(0)=0$. Using a version of the chain rule for fractional derivatives and some estimates on the evolution group, we prove existence, uniqueness and regularity properties of the solution of the equation when the space of the initial data is $H^s(\mathbb{R}), \, s>1/2$. The theorem we prove is sharp. We obtain all the above results also for a mixed KdV and Schrödinger type equation proposed as a model for the propagation of a signal in an optic fiber.

Citation

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Gigliola Staffilani. "On the generalized Korteweg-de Vries-type equations." Differential Integral Equations 10 (4) 777 - 796, 1997.

Information

Published: 1997
First available in Project Euclid: 1 May 2013

zbMATH: 0891.35135
MathSciNet: MR1741772

Subjects:
Primary: 35A07
Secondary: 35B30, 35Q53, 35Q55

Rights: Copyright © 1997 Khayyam Publishing, Inc.

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Vol.10 • No. 4 • 1997
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