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


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations