Advances in Differential Equations

Remarks on the orbital stability of ground state solutions of fKdV and related equations

Felipe Linares, Didier Pilod, and Jean-Claude Saut

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Abstract

The aim of this paper is to provide a proof of the (conditional) orbital stability of solitary waves solutions to the fractional Korteweg-de Vries equation (fKdV) and to the fractional Benjamin-Bona-Mahony (fBBM) equation in the $L^2$ subcritical case. We also discuss instability and its possible scenarios.

Article information

Source
Adv. Differential Equations Volume 20, Number 9/10 (2015), 835-858.

Dates
First available in Project Euclid: 23 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1435064515

Mathematical Reviews number (MathSciNet)
MR3360393

Zentralblatt MATH identifier
1325.35195

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35B35: Stability 76B25: Solitary waves [See also 35C11] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]

Citation

Linares, Felipe; Pilod, Didier; Saut, Jean-Claude. Remarks on the orbital stability of ground state solutions of fKdV and related equations. Adv. Differential Equations 20 (2015), no. 9/10, 835--858. https://projecteuclid.org/euclid.ade/1435064515.


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