| Abstract: | The long-time asymptotic solution of the Korteweg-deVries equation, corresponding to initial data which decay rapidly as |x|→∞ and produce no solitons, is found to be considerably more complicated than previously reported. In general, the asymptotic solution consists of exponential decay, similarity, rapid oscillations and a “collisionless shock” layer. The wave amplitude in this layer decays as (lnt)/t]2/3. Only for very special initial conditions is the shock layer absent from the solution. |
