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

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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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2019-07
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.475, no.1, pp.1 - 12

ISSN
0022-247X
DOI
10.1016/j.jmaa.2018.09.061
URI
http://hdl.handle.net/10203/261701
Appears in Collection
RIMS Journal Papers
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