Solitary waves in atomic chains and peridynamical media. (English) Zbl 1439.35473
Summary: Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of solitary traveling waves for super-quadratic potentials by maximizing the potential energy subject to both a norm and a shape constraint. We also discuss the numerical computation of waves and study several asymptotic regimes.
MSC:
| 35Q82 | PDEs in connection with statistical mechanics |
| 82D20 | Statistical mechanics of solids |
| 82C20 | Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
| 35C08 | Soliton solutions |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B10 | Periodic solutions to PDEs |
| 35R09 | Integro-partial differential equations |
| 45K05 | Integro-partial differential equations |
| 81V45 | Atomic physics |
| 35A15 | Variational methods applied to PDEs |
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