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arXiv · 1508.06123

On the integrability of the sine-Gordon equation

Yannick Widmer
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Abstract

Among other results we show that near the equilibrium point, the Hamiltonian of the sine-Gordon (SG) equation on the circle can be viewed as an element in the Poisson algebra of the modified Korteweg-de Vries (mKdV) equation and hence by well established properties of the latter equation admits Birkhoff coordinates. On the other hand we prove that there exists a large set of smooth initial data, away from the equilibrium point and lying on the ramification locus of a double cover, for which the initial value problem of the SG equation has no classical solution.

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Yannick Widmer. 2015-08-25. On the integrability of the sine-Gordon equation. https://arxiv.org/abs/1508.06123

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