Stability of solitary and cnoidal traveling wave solutions for a fifth order Korteweg-de Vries equation

Ronald Adams and Stefan C. Mancas

Applied Mathematics and Computation, 2018, vol. 321, issue C, 745-751

Abstract: We establish the nonlinear stability of solitary waves (solitons) and periodic traveling wave solutions (cnoidal waves) for a Korteweg-de Vries (KdV) equation which includes a fifth order dispersive term. The traveling wave solutions which yield solitons for zero boundary conditions and wave-trains of cnoidal waves for nonzero boundary conditions are analyzed using stability theorems, which rely on the positivity properties of the Fourier transforms. We show that all families of solutions considered here are (orbitally) stable.

Keywords: Cnodial waves; Solitary waves; Fifth order KdV equation; Stability of traveling waves (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:321:y:2018:i:c:p:745-751

DOI: 10.1016/j.amc.2017.11.005

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