Normal form approach to near-linear dynamics of modified KdV equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Yoon, Haewon^1,2 

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak Ro, Daejeon 34141, South Korea

[2] Natl Taiwan Univ, Math Div, Natl Ctr Theoret Sci, 1 Sec 4 Roosevelt Rd, Taipei 10617, Taiwan

关键词: Modified KdV equation;    Normal form reduction;    Near-linear dynamics;   

DOI  :  10.1016/j.jmaa.2018.09.061

来源: Elsevier

【 摘 要 】

In this paper, we implement normal form reduction to the periodic modified Korteweg-de Vries (mKdV) equation to investigate the behavior of a solution when a subtle high-frequency initial data is given. We use differentiation by parts to decompose the equation into resonant and non-resonant parts and provide some nonlinear estimates for each term. If a subtle high-frequency initial data is given, a solution of the mKdV equation can be approximated by a solution of the linearized mKdV equation for large times. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free