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

• Published in: Acoustical physics Vol. 56; no. 5; pp. 626 - 631
• Main Authors: Gusev, V. A., Makov, Yu. N.
• Format: Journal Article
• Language: English
• 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

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...