Spectral representation of solution of cubically nonlinear equation for the Riemann simple wave

For the implicit solution to the cubically nonlinear equation of the Riemann wave (a simple wave equation), its exact explicit Fourier transform is obtained. The latter corresponds to the transformation of the initial sinusoidal profile until the discontinuity formation and, beyond it, to the asympt...

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Bibliographic Details
Published inAcoustical physics Vol. 56; no. 5; pp. 626 - 631
Main Authors Gusev, V. A., Makov, Yu. N.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.09.2010
Subjects
Acoustics
Asymptotic properties
Constraining
Discontinuity
Fourier transforms
Nonlinear Acoustics
Nonlinear equations
Nonlinearity
Physics
Physics and Astronomy
Spectra
Spectral Representation
Half Period
Acoustical Physic
Spectral Amplitude
Wave Profile
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Summary:For the implicit solution to the cubically nonlinear equation of the Riemann wave (a simple wave equation), its exact explicit Fourier transform is obtained. The latter corresponds to the transformation of the initial sinusoidal profile until the discontinuity formation and, beyond it, to the asymptotic behavior of the same profile at large distances. The significance of the given solutions for the problems with cubic nonlinearity is identical to the significance of the well-known Fubini solution and the limiting version of the Fay solution for conventional nonlinear acoustics.
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ISSN:1063-7710
1562-6865
DOI:10.1134/S1063771010050040