Quasi-periodic Solutions for the Derivative Nonlinear Schrdinger Equation with Finitely Differentiable Nonlinearities

【Author】

Meina GAO;Kangkang ZHANG;School of Sciences, Shanghai Second Polytechnic University;School of Mathematical Sciences, Fudan University;

【Institution】

School of Sciences, Shanghai Second Polytechnic University;School of Mathematical Sciences, Fudan University;

【Abstract】

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.

【Keywords】

Derivative NLS;;KAM theory;;Newton iterative scheme;;Reduction theory;;Quasi-periodic solutions;;Smoothing techniques

References

To explore the background and basis of the node document

Springer Journals Database

Total: 32 articles

  • [1] Jing ZHANG School of Mathematical Sciences, Peking University, Beijing 100871, China, On Lower Dimensional Invariant Tori in C~d Reversible Systems, Chinese Annals of Mathematics, 2008 (05)
  • [2] Massimiliano Berti;;Philippe Bolle, Sobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential, Nonlinearity, 2012 (9)
  • [3] Jiansheng Geng;;Xindong Xu;;Jiangong You, An infinite dimensional KAM theorem and its application to the two dimensional cubic Schr?dinger equation, Advances in Mathematics, 2011 (6)
  • [4] M. Berti;;P. Bolle;;M. Procesi, An abstract Nash–Moser theorem with parameters and applications to PDEs, Annales de l'Institut Henri Poincare / Analyse non lineaire, 2009 (1)

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