Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities

Pages: 835 - 849, Volume 30, Issue 3, July 2011      doi:10.3934/dcds.2011.30.835

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Alexander Pankov - Mathematics Department, Morgan State University, 1700 E Cold Spring Lane, Baltimore, MD 21251, United States (email)
Vassilis M. Rothos - School of Mathematics, Physics and Computational Sciences, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece (email)

Abstract: We prove the existence of periodic and solitary traveling waves in Fermi-Pasta-Ulam lattices with saturable nonlinearities. The approach is based on variational techniques and concentration compactness.

Keywords:  Fermi-Pasta-Ulam lattice, traveling wave, mountain pass theorem, concentration compactness.
Mathematics Subject Classification:  Primary: 37K60; Secondary: 82C20.

Received: December 2009;      Revised: December 2010;      Available Online: March 2011.