Invariant tori for a nonlinearly modified Kawahara equation with periodic boundary conditions

Abstract

Abstract This paper is concerned with a nonlinearly modified Kawahara equation with periodic boundary conditions ut+uxxx−u5x+αu2ux=0. $$ u_{t}+u_{xxx}-u_{5x}+\alpha u^{2}u_{x}=0. $$ Based on an abstract infinite-dimensional KAM theorem for unbounded perturbation vector fields and partial Birkhoff normal form, we prove the existence of n-dimensional invariant tori for the equation.

Keywords

• Nonlinearly modified Kawahara equation
• KAM theorem
• Invariant tori
• Normal form