Schwetlick, Hartmut; Zimmer, Johannes Solitary waves for nonconvex FPU lattices. (English) Zbl 1114.37044 J. Nonlinear Sci. 17, No. 1, 1-12 (2007). 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. Cited in 11 Documents MSC: 37K60 Lattice dynamics; integrable lattice equations 74J35 Solitary waves in solid mechanics 49J35 Existence of solutions for minimax problems Keywords:discrete nonlinear elasticity; nonconvex energy; lattice dynamics; solitary waves; double well PDFBibTeX XMLCite \textit{H. Schwetlick} and \textit{J. Zimmer}, J. Nonlinear Sci. 17, No. 1, 1--12 (2007; Zbl 1114.37044) Full Text: DOI Link