Meina GAO;Kangkang ZHANG;School of Sciences, Shanghai Second Polytechnic University;School of Mathematical Sciences, Fudan University;
School of Sciences, Shanghai Second Polytechnic University;School of Mathematical Sciences, Fudan University;
The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.
Derivative NLS;;KAM theory;;Newton iterative scheme;;Reduction theory;;Quasi-periodic solutions;;Smoothing techniques
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