一维和二维Klein-Gordon格点中小振幅呼吸子的存在性和连续逼近
Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices
摘要：
我们在一维和二维Klein-Gordon无限晶格中构造了小振幅呼吸子。我们还表明，呼吸子很好地近似的基态的非线性薛定谔方程。利用Klein Gordon格与离散非线性Schroedinger格之间的关系得到了这个结果。证明是基于在[7]中引入的Lyapunov-Schmidt分解和连续逼近技术，实际上使用其主要结果作为重要引理。
英文摘要：
We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum approximation techniques introduced in [7], actually using its main result as an important lemma.
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