Lattice solitary traveling waves are nonlinear coherent structures that describe fundamental
mechanisms of energy transport and signal transmission in many physical settings. This …

Ordered granular structures have garnered considerable attention across various fields due
to their capacity to manipulate the transmission of mechanical energy and mitigate the …

Locally resonant metamaterials have recently drawn the attention of many researchers due
to their capability in controlling low-frequency waves by forming a bandgap resulting from …

Traveling waves in woodpile chains are typically nanoptera, which are composed of a
central solitary wave and exponentially small oscillations. These oscillations have been …

Singularly perturbed ordinary differential equations often exhibit Stokes' phenomenon,
which describes the appearance and disappearance of oscillating exponentially small terms …

We use exponential asymptotics to study travelling waves in woodpile systems modelled as
singularly perturbed granular chains with zero precompression and small mass ratio. These …

Exponential small splitting of separatrices in the singular perturbation theory leads generally
to nonvanishing oscillations near a saddle--center point and to nonexistence of a true …

We consider generalizations of nonlinear Schrödinger equations, which we call “Karpman
equations,” that include additional linear higher-order derivatives. Singularly-perturbed …