The periodic Cauchy problem for Novikov's equation
Analysis of PDEs
2010-09-10 v1
Abstract
We study the periodic Cauchy problem for an integrable equation with cubic nonlinearities introduced by V. 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, that establishes the existence and uniqueness of real analytic solutions.
Keywords
Cite
@article{arxiv.1009.1820,
title = {The periodic Cauchy problem for Novikov's equation},
author = {Feride Tiglay},
journal= {arXiv preprint arXiv:1009.1820},
year = {2010}
}