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| We consider an overdamped Frenkel-Kontorova lattice with piecewise linear bistable interaction force due to the onsite potential and harmonic first and second-neighbor interactions that may be either attractive or repulsive. We construct traveling wave solutions that connect various periodic equilibria to the undeformed equilibrium state. Such solutions may be interpreted as steadily propagating fronts of microstructural patterns. Existence, multiplicity and global structure of these solutions are investigated. We show that competing interactions bring interesting new features, such as a maximum speed of propagation and coexistence of multiple traveling waves. |
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