Local well-posedness for the KdV hierarchy at high regularity. (English) Zbl 1375.35449

Kenig, Carlos E.; Pilod, Didier

Adv. Differ. Equ. 21, No. 9-10, 801-836 (2016).

Summary: We prove well-posedness in \(L^2\)-based Sobolev spaces \(H^s\) at high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35A01	Existence problems for PDEs: global existence, local existence, non-existence
37K05	Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35E15	Initial value problems for PDEs and systems of PDEs with constant coefficients
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs