A reducibility technique in quasi-periodic Kdv equation and its applications to .......
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题目：A reducibility technique in quasi-periodic Kdv equation and its applications to quasi-periodic Schr\"odinger operator
摘要：We mainly apply KAM to 1D linear Kdv equation whose coefficients are real analytic, with parity, and bounded above under a suitable norm. Under the periodic boundary condition, we show that there exists a Cantor set, such that it is smoothly reducible to a constant-coefficient one. Our result removes a condition assumed in Baldi-Berti-Montalto-2014 and can yield general existence and linear stability results for quasi-periodic solutions of a reversible, quasi-periodically forced, nonlinear Kdv equation with essentially no restriction on the nonlinearity. Moreover, we can apply the similar technique to quasi-periodic Schr\"odinger operator and explore its spectrum and so on.