January  1996, 2(1): 65-94. doi: 10.3934/dcds.1996.2.65

Normal forms for quasiperiodic evolutionary equations

1. 

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

2. 

Department of Mathematics, Brigham Young University, Provo, Utah 84602, United States

3. 

Department of Mathematics, Western Washington University, Bellingham, WA 98225, United States

Received  February 1995 Published  October 1995

In this paper, we study the normal forms and analytic conjugacy for a class of analytic quasiperiodic evolutionary equations including parabolic equations and Schrödinger equations. We first obtain a normal form theory. Then as a special case of the normal form theory, we show that if the frequency and the eigenvalues satisfy certain small divisor conditions then the nonlinear equation is locally analytically conjugated to a linear equation. In other words, the normal form is a linear equation.
Citation: Shui-Nee Chow, Kening Lu, Yun-Qiu Shen. Normal forms for quasiperiodic evolutionary equations. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 65-94. doi: 10.3934/dcds.1996.2.65
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