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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) $$du/dt+D^ 3u+uDu=0$$, $$t>0$$, $$x\in {\mathbb{R}}$$, $$u(0)=\phi$$, where $$D=d/dx$$. We also consider a generalized KdV equation (G) $$du/dt+D^ 3u+a(u)Du=0$$, $$u(0)=\phi$$, in which a is assumed to be a $$C^{\infty}$$ function on $${\mathbb{R}}$$ to $${\mathbb{R}}$$. 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, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
##### Keywords:
Korteweg-de Vries; Cauchy problems; well posed