KAM Theory for Quasi-periodic Equilibria in One-Dimensional Quasi-periodic Media

2012 ◽  
Vol 44 (6) ◽  
pp. 3901-3927 ◽  
Author(s):  
Xifeng Su ◽  
Rafael de la Llave
Keyword(s):  
Kam Theory ◽  
Periodic Media ◽  
One Dimensional

Gap solitons and their linear stability in one-dimensional periodic media

2011 ◽  
Vol 240 (12) ◽  
pp. 1055-1068 ◽  
Author(s):  
Guenbo Hwang ◽  
T.R. Akylas ◽  
Jianke Yang
Keyword(s):  
Linear Stability ◽  
Periodic Media ◽  
One Dimensional ◽  
Gap Solitons

Bragg diffraction of waves in one-dimensional doubly periodic media

1994 ◽  
Vol 50 (6) ◽  
pp. 3631-3635 ◽  
Author(s):  
F. G. Bass ◽  
G. Ya. Slepyan ◽  
S. T. Zavtrak ◽  
A. V. Gurevich
Keyword(s):  
Bragg Diffraction ◽  
Periodic Media ◽  
One Dimensional

One-Dimensional Periodic Potential in Quantum Mechanics

2010 ◽  
Vol 3 (2) ◽  
pp. 99-107
Author(s):  
Vladimir K. Ignatovich
Keyword(s):  
Mathematical Method ◽  
Quantum Mechanics ◽  
Periodic Potential ◽  
Three Dimensional ◽  
Periodic Systems ◽  
Periodic Media ◽  
One Dimensional

An elegant mathematical method is demonstrated with the help of simplest one-dimensional problems of quantum mechanics. This method is then applied to calculation of scattering on one-dimensional periodic systems. Generalization of the method for calculation of scattering in three dimensional periodic media and for spinor particles is pointed out.

scholarly journals NEW ESTIMATES FOR EVANS' VARIATIONAL APPROACH TO WEAK KAM THEORY

2013 ◽  
Vol 15 (02) ◽  
pp. 1250055 ◽  
Author(s):  
OLGA BERNARDI ◽  
FRANCO CARDIN ◽  
MASSIMILIANO GUZZO
Keyword(s):  
Variational Principle ◽  
Hamiltonian Systems ◽  
Lower Bounds ◽  
Variational Approach ◽  
Degrees Of Freedom ◽  
Kam Theory ◽  
Weak Kam Theory ◽  
One Dimensional ◽  
Dynamic Interpretation ◽  
Geometric Content

We consider a recent approximate variational principle for weak KAM theory proposed by Evans. As in the case of classical integrability, for one-dimensional mechanical Hamiltonian systems all the computations can be carried out explicitly. In this setting, we illustrate the geometric content of the theory and prove new lower bounds for the estimates related to its dynamic interpretation. These estimates also extend to the case of n degrees of freedom.

OPTIMAL BOUNDS ON DISPERSION COEFFICIENT IN ONE-DIMENSIONAL PERIODIC MEDIA

2009 ◽  
Vol 19 (09) ◽  
pp. 1743-1764 ◽  
Author(s):  
CARLOS CONCA ◽  
JORGE SAN MARTÍN ◽  
LOREDANA SMARANDA ◽  
MUTHUSAMY VANNINATHAN
Keyword(s):  
Periodic Structure ◽  
Volume Fraction ◽  
Dispersion Coefficient ◽  
One Dimension ◽  
Periodic Media ◽  
One Dimensional ◽  
Dispersion Tensor ◽  
Optimal Bounds ◽  
Macroscopic Quantity

In this paper, we consider the macroscopic quantity, namely the dispersion tensor associated with a periodic structure in one dimension (see Refs. 5 and 7). We describe the set in which this quantity lies, as the microstructure varies preserving the volume fraction.

Mechanisms of second-harmonic generation in one-dimensional periodic media

1999 ◽  
Vol 29 (7) ◽  
pp. 632-637 ◽  
Author(s):  
Anatolii V Andreev ◽  
O A Andreeva ◽  
A V Balakin ◽  
D Boucher ◽  
P Masselin ◽  
...  
Keyword(s):  
Second Harmonic Generation ◽  
Harmonic Generation ◽  
Second Harmonic ◽  
Periodic Media ◽  
One Dimensional
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