scholarly journals Two-dimensional asynchronous fractional Fourier transform and propagation properties of beams in strongly nonlocal nonlinear medium with an elliptically symmetric response

2013 ◽  
Vol 62 (8) ◽  
pp. 084211
Author(s):  
Lu Da-Quan ◽  
Hu Wei
Keyword(s):  
Fourier Transform ◽  
Nonlinear Medium ◽  
Fractional Fourier Transform ◽  
Two Dimensional ◽  
Propagation Properties ◽  
Symmetric Response ◽  
Nonlocal Nonlinear

scholarly journals Mutual-induced fractional Fourier transform in strongly nonlocal nonlinear medium

2011 ◽  
Vol 60 (8) ◽  
pp. 084214
Author(s):  
Zhao Bao-Ping ◽  
Yang Zhen-Jun ◽  
Lu Da-Quan ◽  
Hu Wei
Keyword(s):  
Fourier Transform ◽  
Nonlinear Medium ◽  
Fractional Fourier Transform ◽  
Nonlocal Nonlinear

scholarly journals Self-accelerating Airy-Laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium

2017 ◽  
Vol 25 (24) ◽  
pp. 30468 ◽  
Author(s):  
Zhenkun Wu ◽  
Zhiping Wang ◽  
Hao Guo ◽  
Wei Wang ◽  
Yuzong Gu
Keyword(s):  
Nonlinear Medium ◽  
Two Dimensional ◽  
Light Bullets ◽  
Nonlocal Nonlinear

scholarly journals The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

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