Trapping light with grating defects
Gap solitons are localized traveling waves that exist in Bragg grating optical fibers. We demonstrate a family of grating defects that support linear and nonlinear standing wave …
Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map
We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink and anti-kink traveling waves of the phi-four …
Strong NLS soliton--defect interactions
We consider the interaction of a nonlinear Schrödinger soliton with a spatially localized (point) defect in the medium through which it travels. Using numerical simulations, we …
Interaction of sine-Gordon kinks with defects: The two-bounce resonance
A model of soliton--defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong …
Trapping of kinks and solitons by defects: phase space transport in finite-dimensional models
We study models of Fei et al. and of Forinash et al of kinks in the sine-Gordon equation, and solitons in the nonlinear Schrodinger equation interacting with point defects. The …
Stopping Light on a Defect
Gap solitons are localized nonlinear coherent states that have been shown both theoretically and experimentally to propagate in periodic structures. Although theory allows for …
Modulations in the leading edges of midlatitude storm tracks
Downstream development is a term encompassing a variety of effects relating to the propagation of storm systems at midlatitude. We investigate a mechanism behind downstream …
Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model
We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a …
Nonlinear propagation of light in one-dimensional periodic structures
We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an …
Trigger Waves in a Model for Catalysis
We consider the model of catalysis due to Ziff, Gulari, and Barshad [Phys Rev. Lett. 56, 2553 (1986)] as a pattern formation problem. We find that the model supports trigger waves …