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Applied Math Seminar The
Traveling waves in lattice dynamical systems |
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We consider the following class of 1-dimensional lattice dynamical systems: chains of particles with nearest neighbour interaction. We prove the existence of spatially periodic traveling waves with prescribed speed and arbitrary period. We also study the asymptotic behavior of such waves for large values of periods and show that they converge in an appropriate topology to a solitary traveling wave. As a concequence, the existence of solitary waves is obtained. |