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Solitary waves for nonconvex FPU lattices. (English) Zbl 1114.37044

Summary: Solitary waves in a one-dimensional chain of atoms \(\{q_j\}_{j\in\mathbb Z}\) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

MSC:

37K60 Lattice dynamics; integrable lattice equations
74J35 Solitary waves in solid mechanics
49J35 Existence of solutions for minimax problems
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