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 [(ln t )/ t ] 2/3 . Only for very special initial conditions is the shock layer absent from the solution.
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Ablowitz et al. (1977) studied this question.