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Remarks on the orbital stability of ground state solutions of fKdV and related equations. (English) Zbl 1325.35195

Summary: 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.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B35 Stability in context of PDEs
76B25 Solitary waves for incompressible inviscid fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35C08 Soliton solutions
26A33 Fractional derivatives and integrals
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