Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations

Pages: 173 - 204, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.173

       Abstract        References        Full Text (427.8K)       Related Articles       

Meina Gao - School of Science, Shanghai Second Polytechnic University, Shanghai 201209, China (email)

Abstract: In this paper, we establish an estimate for the solutions of a small-divisor equation with large variable coefficient. Then by formulating an infinite-dimensional KAM theorem which allows for multiple normal frequencies and unbounded perturbations, we prove that there are many periodic solutions for the derivative nonlinear Schrödinger equations subject to small Hamiltonian perturbations.

Keywords:  KAM theory, derivative nonlinear Schrödinger equation, multiple normal frequencise.
Mathematics Subject Classification:  Primary: 37K55; Secondary: 35Q55.

Received: January 2014;      Revised: April 2014;      Available Online: August 2014.