Benjamin–Feir type instability of Sine–Gordon equation and spectrum of Lamé equation

The Benjamin–Feir type instability of the nonhomoclinic wavetrain solution of the Sine–Gordon equation against the spatially periodic small perturbation is observed by relating the Fourier coefficients of the first order approximate solution of Fourier type to the band structure of the spectrum of t...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 207; no. 2; pp. 345 - 351
Main Authors Ohmiya, M., Ohkura, H., Okaue, D., Saitoh, D., Shiba, T.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 15.10.2007
Elsevier
Subjects
Approximate solution of Fourier type
Benjamin–Feir instability
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Partial differential equations
Sciences and techniques of general use
Sine–Gordon equation
Spectrum of Lamé equation
Wavetrain solution
37K45
33E10
Spectrum of Lamé equation
Wavetrain solution
Benjamin–Feir instability
35Q53
Sine–Gordon equation
Approximate solution of Fourier type
35Q53; 33E10; 37K45
Fourier analysis
Numerical analysis
Sine-Gordon equation; Benjamin-Feir instability; Wavetrain solution; Approximate solution of Fourier type; Spectrum of Lamé equation
Fourier coefficient
Applied mathematics
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Summary:The Benjamin–Feir type instability of the nonhomoclinic wavetrain solution of the Sine–Gordon equation against the spatially periodic small perturbation is observed by relating the Fourier coefficients of the first order approximate solution of Fourier type to the band structure of the spectrum of the Lamé equation.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.10.009