We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov and Xu, we prove that such solutions exist in two distinguished limits; the first where the mass of the internal resonator is small and the second where the internal spring is very stiff. We then numerically simulate the solutions, and these simulations indicate that the anti-resonant traveling waves are very weakly unstable.

中文翻译：

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质量块中的孤波

我们考虑质量块晶格的空间局部行波解的存在。在Kevrekidis，Stefanov和Xu首次发现的反共振条件下，我们证明了这样的解决方案存在两个显着的限制：第一个内部谐振器的质量很小，第二个内部弹簧非常坚硬。然后，我们对解决方案进行了数值模拟，这些模拟表明反共振行波非常不稳定。