On singularity of a nonlinear variational sine-Gordon equation |
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Authors: | Kyungwoo Song |
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Affiliation: | Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, USA |
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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. |
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