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On the Cauchy problem for the (generalized) Korteweg-de Vries equation. (English) Zbl 0549.34001
Adv. Math., Suppl. Stud. 8, 93-128 (1983).
From author’s summary: ”We consider the Cauchy problem for the Korteweg- de Vries (KdV) equation (K) $du/dt+{D}^{3}u+uDu=0$, $t>0$, $x\in ℝ$, $u\left(0\right)=\phi$, where $D=d/dx$. We also consider a generalized KdV equation (G) $du/dt+{D}^{3}u+a\left(u\right)Du=0$, $u\left(0\right)=\phi$, in which a is assumed to be a ${C}^{\infty }$ function on $ℝ$ to $ℝ$. Our main object is to show that the Cauchy problems for (K) and (G) are well posed.”
Reviewer: H.Fiedler

##### MSC:
 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions
##### Keywords:
Korteweg-de Vries; Cauchy problems; well posed