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

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