Gao, Mei Na et Zhang, Jing, Small-divisor equation of higher order with large variable coefficient and application to the coupled KdV equation, Acta mathematica Sinica. English series (Print) , 27(10), 2011, pp. 2005-2032
In this paper, we establish an estimate for the solutions of small-divisor equation of higher order with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the coupled KdV equation subject to small Hamiltonian perturbations.