Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 3

Invariant tori for a fifth order nonlinear partial differential equation with unbounded perturbation

Pages: 183 – 199

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n3.a2

Authors

Wenyan Cui (College of Science, Binzhou University, Shandong, China)

Lufang Mi (College of Science, Binzhou University, Shandong, China)

Jumei Zhang (College of Science, Binzhou University, Shandong, China)

Li Yin (College of Science, Binzhou University, Shandong, China)

Abstract

In this paper, we are concerned with small perturbation of the nonlinear partial differential equation\[u_t = u_{5x} - \frac{5}{16} (8u^2_{xx} + 8u_x u_{xxx})\]under periodic boundary conditions. Using an abstract infinite dimensional KAM theorem, we obtain the existence of many two-dimensional invariant tori and thus many time quasi-periodic solutions for the above equation under sufficiently small Hamiltonian perturbation.

Keywords

quasi-periodic solution, KAM theory, normal form

2010 Mathematics Subject Classification

35Q55, 37K55

Full Text (PDF format)

Supported by NNSFC (11401041)(11601036), the University Science and Technology Foundation of Shandong Province Education Department (J14LI54) and Binzhou University (BZXYL1406).

Received 5 November 2017

Published 29 May 2018