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March 2004 Stablity of solitary waves in higher order Sobolev spaces
Jerry L. Bona, Yue Liu, Nghiem V. Nguyen
Commun. Math. Sci. 2(1): 35-52 (March 2004).


The orbital stability of solitary waves has generally been established in Sobolev classes of relatively low order, such as $H^1$. It is shown here that at least for solitary-wave solutions of certain model equations, a sharp form of orbital stability is valid in $L^2$-based Sobolev classes of arbitrarily high order. Our theory includes the classical Korteweg-de Vries equation, the Benjamin- Ono equation and the cubic, nonlinear Schrödinger equation.


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Jerry L. Bona. Yue Liu. Nghiem V. Nguyen. "Stablity of solitary waves in higher order Sobolev spaces." Commun. Math. Sci. 2 (1) 35 - 52, March 2004.


Published: March 2004
First available in Project Euclid: 21 August 2009

zbMATH: 1089.35057
MathSciNet: MR2082818

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 1 • March 2004
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