Differential and Integral Equations

Long-period limit of nonlinear dispersive waves: the BBM-equation

Hongqiu Chen

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Abstract

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 $l\to\infty.$

Article information

Source
Differential Integral Equations, Volume 19, Number 4 (2006), 463-480.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050509

Mathematical Reviews number (MathSciNet)
MR2215629

Zentralblatt MATH identifier
1212.35406

Subjects
Primary: 35B10
Secondary: 35L05: Wave equation 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30} 42A20: Convergence and absolute convergence of Fourier and trigonometric series 45G10: Other nonlinear integral equations 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]

Citation

Chen, Hongqiu. Long-period limit of nonlinear dispersive waves: the BBM-equation. Differential Integral Equations 19 (2006), no. 4, 463--480. https://projecteuclid.org/euclid.die/1356050509


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