On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation

Persistence of spatial analyticity is studied for periodic solutions of the dispersion-generalized KdV equation ut−|Dx|αux+uux=0 for α≥2. For a class of analytic initial data with a uniform radius of analyticity σ0>0, we obtain an asymptotic lower bound σ(t)≥ct−p on the uniform radius of analyticity σ(t) at time t, as t→∞, where p=max(1,4/α). The proof relies on bilinear estimates in Bourgain spaces and an approximate conservation law.