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- W4300842023 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." @default.
- W4300842023 created "2022-10-04" @default.
- W4300842023 creator A5003815574 @default.
- W4300842023 date "2010-09-09" @default.
- W4300842023 modified "2023-09-24" @default.
- W4300842023 title "The periodic Cauchy problem for Novikov's equation" @default.
- W4300842023 doi "https://doi.org/10.48550/arxiv.1009.1820" @default.
- W4300842023 hasPublicationYear "2010" @default.
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