Local well-posedness for the periodic higher order KdV type equations

Abstract

Higher order KdV type equations are the equation replaced by a higher order derivative \({\partial_{x}^{2k+1}}\) for the KdV equation. Recently, the local well-posedness result for these equations on torus have been given by Gorsky and Himonas (Math. Comput. Simul. 80:173–183, 2009). We extend this result by improving a bilinear estimate used in the Fourier restriction norm method.