Multiple-time-scale perturbation theory applied to laser excitation of atoms and molecules

1976 ◽  
Vol 13 (2) ◽  
pp. 674-687 ◽  
Author(s):  
J. Wong ◽  
J. C. Garrison ◽  
T. H. Einwohner
Keyword(s):  
Perturbation Theory ◽  
Time Scale ◽  
Laser Excitation ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Atoms And Molecules ◽  
Scale Perturbation

Breather structures in degenerate relativistic non-extensive plasma

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
M. Shahmansouri ◽  
H. Alinejad ◽  
M. Tribeche
Keyword(s):  
Time Scale ◽  
Perturbation Technique ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Astrophysical Plasmas ◽  
Plasma System ◽  
Localized Solutions ◽  
Nonlinear Excitations ◽  
Scale Perturbation ◽  
Basic Features

We examine the excitation of breather structures in a degenerate relativistic plasma consisting of non-extensive electrons and cold ions. For this purpose, the multiple time scale perturbation technique is used to obtain a nonlinear Schrödinger equation (NLSE). We then consider different localized solutions regarding analytical breather solutions of the NLSE, and examine their properties in the frame of the present plasma system, i.e. a degenerate relativistic non-extensive plasma. The results of the present investigation may be useful for the understanding of the basic features of the nonlinear excitations that may occur in dense astrophysical plasmas.

BIFURCATIONS OF RELAXATION OSCILLATIONS NEAR FOLDED SADDLES

2005 ◽  
Vol 15 (11) ◽  
pp. 3411-3421 ◽  
Author(s):  
JOHN GUCKENHEIMER ◽  
KATHLEEN HOFFMAN ◽  
WARREN WECKESSER
Keyword(s):  
Perturbation Theory ◽  
Dynamical Systems ◽  
Singular Perturbation ◽  
Time Scale ◽  
Singular Limit ◽  
Singular Perturbation Theory ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Relaxation Oscillations ◽  
Geometric Methods

Relaxation oscillations are periodic orbits of multiple time scale dynamical systems that contain both slow and fast segments. The slow–fast decomposition of these orbits is defined in the singular limit. Geometric methods in singular perturbation theory classify degeneracies of these decompositions that occur in generic one-parameter families of relaxation oscillations. This paper investigates the bifurcations that are associated with one type of degeneracy that occurs in systems with two slow variables, in which relaxation oscillations become homoclinic to a folded saddle.

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