Applied Mathematics and Mathematical Physics Seminar: Feride Tiglay

Abstract
We study the periodic Cauchy problem for an integrable equation with cubic nonlinearities introduced by Novikov. Like the Camassa–Holm and Degasperis–Procesi equations, Novikov’s equation has Lax pair representations and admits peakon solutions, but it has nonlinear terms that are cubic, rather than quadratic. We show the local well-posedness of the problem in Sobolev spaces and existence and uniqueness of solutions for all time using orbit invariants. Furthermore, we prove a Cauchy–Kowalevski type theorem for this equation, which establishes the existence and uniqueness of real analytic solutions.