scholarly journals Diffractons: Solitary Waves Created by Diffraction in Periodic Media

2015 ◽  
Vol 13 (1) ◽  
pp. 440-458 ◽  
Author(s):  
David I. Ketcheson ◽  
Manuel Quezada de Luna
Keyword(s):  
Solitary Waves ◽  
Periodic Media

scholarly journals From non-local gap solitary waves to bound states in periodic media

2011 ◽  
Vol 468 (2137) ◽  
pp. 116-135 ◽  
Author(s):  
T. R. Akylas ◽  
Guenbo Hwang ◽  
Jianke Yang
Keyword(s):  
Solitary Waves ◽  
Bound States ◽  
Wave Spectrum ◽  
Separation Distance ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Periodic Media ◽  
Non Local ◽  
Gap Solitons ◽  
Power Curves

Solitary waves in one-dimensional periodic media are discussed by employing the nonlinear Schrödinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of Bloch bands in the linear wave spectrum. These fundamental solitons may be positioned only at specific locations relative to the potential; otherwise, they become non-local owing to the presence of growing tails of exponentially small amplitude with respect to the wave peak amplitude. Here, by matching the tails of such non-local solitary waves, high-order locally confined gap solitons, or bound states, are constructed. Details are worked out for bound states comprising two non-local solitary waves in the presence of a sinusoidal potential. A countable set of bound-state families, characterized by the separation distance of the two solitary waves, is found, and each family features three distinct solution branches that bifurcate near Bloch-band edges at small, but finite, amplitude. Power curves associated with these solution branches are computed asymptotically for large solitary-wave separation, and the theoretical predictions are consistent with numerical results.

scholarly journals Numerical Simulation of Cylindrical Solitary Waves in Periodic Media

2013 ◽  
Vol 58 (3) ◽  
pp. 672-689 ◽  
Author(s):  
Manuel Quezada de Luna ◽  
David I. Ketcheson
Keyword(s):  
Numerical Simulation ◽  
Solitary Waves ◽  
Periodic Media

Solitary waves on manifolds of integrate-and-fire neurons

1998 ◽  
Vol 77 (5) ◽  
pp. 1575-1583
Author(s):  
David Horn, Irit Opher
Keyword(s):  
Solitary Waves ◽  
Integrate And Fire

Nonlinear Pulse Propagation and Modulation Instability in Periodic Media with and without Defects

PIERS Online ◽  
2006 ◽  
Vol 2 (2) ◽  
pp. 177-181
Author(s):  
V. Grimalsky ◽  
Svetlana Koshevaya ◽  
Javier Sanchez-Mondragon ◽  
Margarita Tecpoyotl Torres ◽  
J. Escobedo Alatorre
Keyword(s):  
Pulse Propagation ◽  
Modulation Instability ◽  
Periodic Media ◽  
Nonlinear Pulse Propagation
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