On singularity of a nonlinear variational sine-Gordon equation

Kyungwoo Song

doi:10.1016/S0022-0396(02)00150-X

On singularity of a nonlinear variational sine-Gordon equation

Kyungwoo Song

Research output: Contribution to journal › Review article › peer-review

10 Citations (Scopus)

Abstract

We study a sine-Gordon-type of nonlinear variational wave equation whose wave speed is a sinusoidal function of the wave amplitude. This equation arises naturally from long waves on a dipole chain in the continuum limit, which provides a crude model for some polymers. Using characteristic methods, we describe a blow-up result for the one-dimensional nonlinear variational sine-Gordon equation, which shows that smooth solutions breakdown in finite time.

Original language	English
Pages (from-to)	183-198
Number of pages	16
Journal	Journal of Differential Equations
Volume	189
Issue number	1
DOIs	https://doi.org/10.1016/S0022-0396(02)00150-X
Publication status	Published - 20 Mar 2003

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AB - We study a sine-Gordon-type of nonlinear variational wave equation whose wave speed is a sinusoidal function of the wave amplitude. This equation arises naturally from long waves on a dipole chain in the continuum limit, which provides a crude model for some polymers. Using characteristic methods, we describe a blow-up result for the one-dimensional nonlinear variational sine-Gordon equation, which shows that smooth solutions breakdown in finite time.

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On singularity of a nonlinear variational sine-Gordon equation

Abstract

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