This paper considers the stabilily of the Korteweg-de Vries solitary wave solutionwith respect to infinitesmal dislurbance.It is found that the Korteweg-de Vries solitarywave solulion is unstable in the Liapunov sense.
Jeffrey Alan and Tsunehiko Kakutani,Stability of the Burgers shock wave and the Korteweg de-Vries solution,Indiana UniversiW Mathematics,20,5(1970),463-468.
[2]
Jeffrey,Alan and Tsunehiko Kakutani,Weak nonlinear dispersive waves:A discussion centered around the korteweg-de vries equation,SIAM Rev.,14(1972),582-643.