Quasi-Periodic Solutions for the Reversible Derivative Nonlinear Schrödinger Equations with Periodic Boundary Conditions

被引：0
作者：
Zhaowei Lou
Jianguo Si
机构：
[1] Shandong University,School of Mathematics
来源：
Journal of Dynamics and Differential Equations | 2017年 / 29卷
关键词：
DNLS; Periodic boundary conditions; Quasi-periodic solution; KAM theorem; Reversible vector field; 37K55; 35Q41; 35B15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove the existence of small amplitude, smooth time quasi-periodic solutions for a class of reversible derivative nonlinear Schrödinger equations with periodic boundary conditions. The proof is based on an abstract Kolmogorov–Arnold–Moser(KAM) theorem for infinite dimensional reversible system.
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页码：1031 / 1069
页数：38
相关论文
共 51 条
  • [1] Baldi P(2014)KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation Math. Ann. 359 471-536
  • [2] Berti M(2014)KAM for quasi-linear KdV C. R. Math. Acad. Sci. Paris 352 603-607
  • [3] Montalto R(2013)KAM theory for the Hamiltonian derivative wave equation Ann. Sci. Éc. Norm. Supér. 46 301-373
  • [4] Baldi P(2014)KAM for reversible derivative wave equations Arch. Ration. Mech. Anal. 212 905-955
  • [5] Berti M(2007)A KAM theorem for reversible systems of infinite dimension Acta Math. Sin. 23 1777-1796
  • [6] Montalto R(2000)KAM tori for 1D nonlinear wave equations with periodic boundary conditions Commun. Math. Phys. 211 497-525
  • [7] Berti M(2010)KAM for the nonlinear Schrödinger equation Ann. Math. 172 371-435
  • [8] Biasco L(2012)Real analytic quasi-periodic solutions for the derivative nonlinear Schrödinger equations J. Math. Phys. 53 102702,27-56
  • [9] Procesi M(2005)A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions J. Differ. Equ. 209 1-372
  • [10] Berti M(2006)A KAM theorem for Hamiltonian partial differential equations in higher dimensional spaces Commun. Math. Phys. 262 343-427
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