Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe

  title={Semiclassical Limit for Generalized KdV Equations Before the Gradient Catastrophe},
  author={Davide Masoero and Andrea Raimondo},
  journal={Letters in Mathematical Physics},
We study the semiclassical limit of the (generalized) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In particular, we show that in the semiclassical limit the solution of the KdV equation: i) converges in Hs to the solution of the Hopf equation, provided the initial data belongs to Hs, ii) admits an asymptotic expansion in powers of the semiclassical parameter, if the initial data belongs to the Schwartz class… 

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  • J. BonaR. Smith
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1975
For the Korteweg-de Vries equation ut+ux+uux+uxxx=0, existence, uniqueness, regularity and continuous dependence results are established for both the pure initial-value problem (posed on -∞<x<∞) and