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2006 Long-period limit of nonlinear dispersive waves: the BBM-equation
Hongqiu Chen
Differential Integral Equations 19(4): 463-480 (2006). DOI: 10.57262/die/1356050509


The focus of the present study is the standard BBM equation which models unidirectional propagation of small amplitude long waves in dispersive media. The equation is posed on the entire real line and the interest here is the relationship between two different types of solutions. The problem has been studied with initial data in various Sobolev spaces defined on $\mathbb R$ and for periodic initial data, say of period $2l.$ The principal new result is an exact theory of convergence of the periodic solutions to the solutions in Sobolev spaces as $l\to\infty.$


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Hongqiu Chen. "Long-period limit of nonlinear dispersive waves: the BBM-equation." Differential Integral Equations 19 (4) 463 - 480, 2006.


Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35406
MathSciNet: MR2215629
Digital Object Identifier: 10.57262/die/1356050509

Primary: 35B10
Secondary: 35L05 , 35Q53 , 42A16 , 42A20 , 45G10 , 76B15

Rights: Copyright © 2006 Khayyam Publishing, Inc.

Vol.19 • No. 4 • 2006
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