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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.

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