Abstract
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.
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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)
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Gao, M.N., Zhang, J. Small-divisor equation of higher order with large variable coefficient and application to the coupled KdV equation. Acta. Math. Sin.-English Ser. 27, 2005–2032 (2011). https://doi.org/10.1007/s10114-011-0064-1
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DOI: https://doi.org/10.1007/s10114-011-0064-1