低维周期Klein-Gordon格的近可积性
Near-integrability of low dimensional periodic Klein-Gordon lattices
摘要：
研究了低维周期Klein-Gordon格的可积性。证明了具有一定非线性势的双粒子周期格是不可积的。然而，在多达六个粒子的情况下，我们证明了它们的Birkhoff-Gustavson规范形式是可积的，这使得我们可以应用KAM理论。
英文摘要：
The low dimensional periodic Klein-Gordon lattices are studied for integrability. We prove that the periodic lattice with two particles and certain nonlinear potential is non integrable. However, in the cases of up to six particles, we prove that their Birkhoff-Gustavson normal forms are integrable, which allows us to apply KAM theory.
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