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October  2011, 4(5): 975-994. doi: 10.3934/dcdss.2011.4.975

## Asymptotics for supersonic traveling waves in the Morse lattice

 1 Department of Mathematics, Southern Methodist University, Dallas TX 75275, United States 2 Department of Mathematics, ESFM-Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F., Mexico 3 FENOMEC, Department of Mathematics and Mechanics, IIMAS-UNAM, Apdo. 20-726, 01000 México D.F., Mexico

Received  August 2009 Revised  December 2009 Published  December 2010

Supersonic traveling wave solutions to the Morse lattice are considered. By numerical means, we show that initial shock like initial values always evolve into traveling shock solutions after the emission of radiation traveling at the sound speed. Using a trial function which includes a shape modulation in the core of the shock we show how the Peierls-Nabarro self consistent potential induced by the lattice is canceled by the adjustment of the phase. We find excellent agreement between the modulation analysis and the numerical solutions.
Citation: Alejandro B. Aceves, Luis A. Cisneros-Ake, Antonmaria A. Minzoni. Asymptotics for supersonic traveling waves in the Morse lattice. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 975-994. doi: 10.3934/dcdss.2011.4.975
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