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.
|Number of pages||28|
|Journal||Mathematics in Engineering|
|Publication status||Published - 7 Mar 2019|
- 37K40, 37K60, 47J30, 74J30, 74H15