Analyticity of solutions of the Korteweg-de Vries equation
The smoothing effect is one of the important properties of the dispersive equation such as the KdV equation. This effect says that solutions gain smoothness if the initial value decays rapidly. The author studies the analytic smoothing effect for the KdV equation. He shows this effect by using the inverse scattering method which transforms the KdV equation to a linear dispersive equation whose analytic smoothing effect is shown through the properties of the Airy function.
scientific article; zbMATH DE number 2139633