scholarly journals Justification of the asymptotic coupled mode approximation of out-of-plane gap solitons in Maxwell equations

Nonlinearity ◽  
2021 ◽  
Vol 34 (8) ◽  
pp. 5261-5318
Author(s):  
Tomáš Dohnal ◽  
Giulio Romani
2005 ◽  
Vol 71 (5) ◽  
Author(s):  
Boris A. Malomed ◽  
Thawatchai Mayteevarunyoo ◽  
Elena A. Ostrovskaya ◽  
Yuri S. Kivshar

Author(s):  
Tomáš Dohnal ◽  
Lisa Wahlers

AbstractWe consider a system of first order coupled mode equations in $${\mathbb {R}}^d$$ R d describing the envelopes of wavepackets in nonlinear periodic media. Under the assumptions of a spectral gap and a generic assumption on the dispersion relation at the spectral edge, we prove the bifurcation of standing gap solitons of the coupled mode equations from the zero solution. The proof is based on a Lyapunov–Schmidt decomposition in Fourier variables and a nested Banach fixed point argument. The reduced bifurcation equation is a perturbed stationary nonlinear Schrödinger equation. The existence of solitary waves follows in a symmetric subspace thanks to a spectral stability result. A numerical example of gap solitons in $${\mathbb {R}}^2$$ R 2 is provided.


2020 ◽  
Vol 269 (3) ◽  
pp. 2386-2418
Author(s):  
Tomáš Dohnal ◽  
Lisa Wahlers

2011 ◽  
Vol 83 (6) ◽  
Author(s):  
Rong Dong ◽  
Christian E. Rüter ◽  
Detlef Kip ◽  
Jesús Cuevas ◽  
Panayotis G. Kevrekidis ◽  
...  

Author(s):  
G.A. Bertero ◽  
R. Sinclair

Pt/Co multilayers displaying perpendicular (out-of-plane) magnetic anisotropy and 100% perpendicular remanent magnetization are strong candidates as magnetic media for the next generation of magneto-optic recording devices. The magnetic coercivity, Hc, and uniaxial anisotropy energy, Ku, are two important materials parameters, among others, in the quest to achieving higher recording densities with acceptable signal to noise ratios (SNR). The relationship between Ku and Hc in these films is not a simple one since features such as grain boundaries, for example, can have a strong influence on Hc but affect Ku only in a secondary manner. In this regard grain boundary separation provides a way to minimize the grain-to-grain magnetic coupling which is known to result in larger coercivities and improved SNR as has been discussed extensively in the literature for conventional longitudinal recording media.We present here results from the deposition of two Pt/Co/Tb multilayers (A and B) which show significant differences in their coercive fields.


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