A higher dispersion KdV equation on the line (Q2199982)

The authors study the well-posedness of the Cauchy problem for the higher dispersion KdV equation \[\partial_tu+(-1)^{j+1}\partial_x^{2j+1}u+\frac12\partial_x(u^2)=0\] in the scales of Sobolev and Gevrey spaces. The approach involves modified bilinear estimates in the Bourgain spaces. Optimality of the estimates is discussed as well as lack of time analyticity.