scholarly journals Study of q-Garnier System by Padé Method

2018 ◽  
Vol 61 (1) ◽  
pp. 109-133 ◽  
Author(s):  
Hidehito Nagao ◽  
Yasuhiko Yamada
Keyword(s):  
Garnier System ◽  
Padé Method

Solutions of the Faddeev equations with local interactions by a variational Padé method

1972 ◽  
Vol 4 (12) ◽  
pp. 561-570 ◽  
Author(s):  
C. Alabiso ◽  
G. Botta ◽  
P. Butera ◽  
G. M. Prosperi
Keyword(s):  
Local Interactions ◽  
Faddeev Equations ◽  
Padé Method

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

Bi-Hamiltonian field Garnier system

1993 ◽  
Vol 174 (1-2) ◽  
pp. 85-88 ◽  
Author(s):  
Maciej Błaszak
Keyword(s):  
Garnier System

Characterizing flat-top laser beams using standard beam parameters

2006 ◽  
Vol 84 (3) ◽  
pp. 223-240 ◽  
Author(s):  
S Saghafi ◽  
M J Withford ◽  
Z Ghoranneviss
Keyword(s):  
Near Field ◽  
Analytical Models ◽  
Model Parameters ◽  
Fourth Moment ◽  
Output Beam ◽  
Field Versus ◽  
Kurtosis Parameter ◽  
Beam Characteristic ◽  
Padé Method ◽  
Beam Parameters

We examine the correspondence between various models describing flat-top laser beam profiles using two standard parameters; namely, the M2 factor and the kurtosis parameter. Numerical expressions for M2, based on the second moment of the beam irradiance distribution in the near and far fields and for the kurtosis parameter, k, based on the fourth moment at the near field, are obtained. Plots of k in the near field versus M2 demonstrate the similarities between the different analytical models used to describe flat-top profiles. Using the Padé approximation, a relationship between k and M2, a new reference formula, is derived that predicts the values of M2 to within less than a percent for these flattened beams. This method is then extended to define numerical expressions relating the beam parameters (i.e., M2 and k) and the parameters describing the beam characteristic in each analytical model (model parameters). The results obtained using the Padé method are used to describe the output beam profiles for a high power copper vapour laser fitted with an unstable resonator.PACS Nos.: 42.55.–f, 42.55.Lt, 42.60.–v

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