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arXiv · 1806.06921

A complete classification of finite Morse index solutions to elliptic sine-Gordon equation in the plane

Yong Liu·Juncheng Wei
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Abstract

The elliptic sine-Gordon equation in the plane has a family of explicit multiple-end solutions (soliton-like solutions). We show that all the finite Morse index solutions belong to this family. We also prove they are non-degenerate in the sense that the corresponding linearized operators have no nontrivial bounded kernel. We then show that solutions with $2n$ ends have Morse index $n(n-1)/2.$

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Yong Liu, Juncheng Wei. 2018-06-18. A complete classification of finite Morse index solutions to elliptic sine-Gordon equation in the plane. https://arxiv.org/abs/1806.06921

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