Evolution of Polarization Singularities of Two Monochromatic Beams in Their Collinear Interaction in an Isotropic Medium with Spatial Dispersion of Cubic Nonlinearity

2017 ◽  
pp. 71-83
Author(s):  
Vladimir Makarov
Keyword(s):  
Isotropic Medium ◽  
Spatial Dispersion ◽  
Cubic Nonlinearity

Chirped elliptically polarised cnoidal waves and polarisation 'chaos' in an isotropic medium with spatial dispersion of cubic nonlinearity

2012 ◽  
Vol 42 (12) ◽  
pp. 1118-1122 ◽  
Author(s):  
Vladimir A Makarov ◽  
V M Petnikova ◽  
N N Potravkin ◽  
Vladimir V Shuvalov
Keyword(s):  
Isotropic Medium ◽  
Spatial Dispersion ◽  
Cubic Nonlinearity ◽  
Cnoidal Waves

Elliptically polarised cnoidal waves in a medium with spatial dispersion of cubic nonlinearity

2012 ◽  
Vol 42 (2) ◽  
pp. 117-119 ◽  
Author(s):  
Vladimir A Makarov ◽  
I A Perezhogin ◽  
V M Petnikova ◽  
N N Potravkin ◽  
Vladimir V Shuvalov
Keyword(s):  
Spatial Dispersion ◽  
Cubic Nonlinearity ◽  
Cnoidal Waves

BIREFRINGENGE INDUCED BY SPATIAL DISPERSION IN ALKALI HALIDES

1985 ◽  
Vol 46 (C7) ◽  
pp. C7-475-C7-478
Author(s):  
C. López ◽  
C. Zaldo ◽  
F. Meseguer
Keyword(s):  
Spatial Dispersion ◽  
Alkali Halides

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

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