摘要
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.
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.
基金
Supported by National Natural Science Foundation of China （Grant No. 10725103）, 973 Program （Grant No 2010CB327900） and Research Foundation for Doctor Programme （Grant No. 20080246） The authors are indebted to X. Yuan for his helpful discussion and encouragements, and to the two reviewers for invaluable suggestions.
