Long-Time Asymptotics for Integrable Nonlinear Wave Equations

We recall the remarkable discovery of Gardner, Green, Kruskal and Miura [9]. Consider the solution of the Korteweg de Vries (KdV) equation $${{q}_{t}} - 6q{{q}_{x}} + {{q}_{{xxx}}} = 0$$ (0.1) with initial data $$q(x,0) = {{q}_{0}}(x) \in \mathcal{S}(R).$$ (0.2)

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