mKdV自治拟线性扰动的KAM
KAM for autonomous quasi-linear perturbations of mKdV
摘要：
证明了mKdV方程的拟线性（也称为强非线性）自治Hamilton可微扰动的小振幅线性稳定拟周期解的Cantor族的存在性.证明是基于一个弱版本的Birkhoff标准形算法和非线性Nash-Moser迭代。通过伪微分算子技术和线性KAM约简方案，分析了迭代过程中每一步的线性化算子。
英文摘要：
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is based on a weak version of the Birkhoff normal form algorithm and a nonlinear Nash-Moser iteration. The analysis of the linearized operators at each step of the iteration is achieved by pseudo-differential operator techniques and a linear KAM reducibility scheme.
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