Well posedness for a higher order modified Camassa–Holm equation

We show that the Cauchy problem for a higher order modification of the Camassa–Holm equation is locally well posed for initial data in the Sobolev space Hs(R) for s>s′, where 1/4⩽s′<1/2 and the value of s′ depends on the order of equation. Employing harmonic analysis methods we derive the corresponding bilinear estimate and then use a contraction mapping argument to prove existence and uniqueness of solutions.