Solutions of the Korteweg-de Vries equation with steplike initial data
The Cauchy problem for the Korteweg-de Vries equation is considered where the initial profile u is a steplike function (i.e. there exist a,b in \({\mathbb{R}}\) such that \[ \int^{0}_{-\infty}| u(x)-a| (1+| x|)^ N dx<\infty \quad and\quad \int^{\infty}_{0}| u(x)- b| (1+| x|)^ N dx<\infty). \] Classical solutions are constructed for \(N\geq 3\).
scientific article; zbMATH DE number 3964569
scientific article