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, Volume 28, Issue 1–3, pp 89–99 | Cite as

On the Korteweg-de Vries equation

  • Tosio Kato


Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function ϕ in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s=∞ being included For the proper KdV equation, existence of global solutions follows if s≥2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere.


Initial Data Evolution Equation Sobolev Space Number Theory Algebraic Geometry 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Tosio Kato
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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