Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane
Classification of finite Morse index solutions to the elliptic sine-Gordon equation in the plane
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DOI：
10.4171/rmi/1296
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Yong Liu;Juncheng Wei
中科院分区：
文献类型：
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作者：
Yong Liu;Juncheng Wei
椭圆型sine-Gordon方程是一个具有特殊双势阱的半线性椭圆型方程。它有一族显式的多端解。我们证明了所有的有限莫尔斯指数解都属于这个族。也将证明这些解是非退化的，在这个意义上，相应的线性化算子没有非平凡的有界核。最后证明了2n-端解的莫尔斯指数等于n（n-1）/2.
The elliptic sine-Gordon equation is a semilinear elliptic equation with a special double well potential. It has a family of explicit multiple-end solutions. We show that all the finite Morse index solutions belong to this family. It will also be proved that these solutions are nondegenerate, in the sense that the corresponding linearized operators have no nontrivial bounded kernel. Finally, we prove that the Morse index of 2n-end solutions is equal to n(n−1)/2.