scholarly journals Analytical solutions of generalized differential equations using quadratic-phase Fourier transform

2021 ◽  
Vol 7 (2) ◽  
pp. 1925-1940
Author(s):  
Firdous A. Shah ◽  
◽  
Waseem Z. Lone ◽  
Kottakkaran Sooppy Nisar ◽  
Amany Salah Khalifa ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Wave Equations ◽  
Preliminary Results ◽  
Quadratic Phase ◽  
Generalized Differential

<abstract><p>The aim of this study is to obtain the analytical solutions of some prominent differential equations including the generalized Laplace, heat and wave equations by using the quadratic-phase Fourier transform. To facilitate the narrative, we formulate the preliminary results vis-a-vis the differentiation properties of the quadratic-phase Fourier transform. The obtained results are reinforced with illustrative examples.</p></abstract>

scholarly journals The Analytical Solution of Parabolic Volterra Integro- Differential Equations in the Infinite Domain

2016 ◽  
Author(s):  
Yun Zhao ◽  
Feng-Qun Zhao
Keyword(s):  
Fourier Transform ◽  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Kernel Functions ◽  
Infinite Domain ◽  
Memory Kernel ◽  
One Dimensional ◽  
Different Types ◽  
Frictional Memory Kernel

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

scholarly journals Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yong-Ju Yang ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Fourier Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Present Method ◽  
Fractional Derivatives ◽  
Wave Equations ◽  
Series Method ◽  
Fourier Series Method ◽  
Fractional Differential

The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.

scholarly journals On New Solutions of System of Shallow Water Wave Equations

2019 ◽  
Vol 7 (6) ◽  
Author(s):  
Ziad Salem Rached
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Wave Equations ◽  
Nonlinear Differential Equations ◽  
Shallow Water Wave ◽  
Shallow Water Wave Equations ◽  
Modified Simple Equation Method

Obtaining analytical solutions of nonlinear differential equations and nonlinear systems of partial and ordinary differential equations is an important topic in various fields of Mathematics. Many techniques are available in the literature. In this note, the enhanced modified simple equation method (EMSEM) is applied to system of shallow water wave equations.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wei Tan ◽  
Zhao-Yang Yin
Keyword(s):  
Differential Equations ◽  
Wave Equations ◽  
Rogue Wave ◽  
Nonlinear Partial Differential Equations ◽  
Rogue Waves ◽  
Homoclinic Solutions ◽  
Nonlinear Wave Equations ◽  
Bilinear Method ◽  
Wave Solutions ◽  
Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Symbolic analytical solutions for the abundances differential equations of the Helium burning phase

2003 ◽  
Vol 324 (5) ◽  
pp. 432-436 ◽  
Author(s):  
M.I. Nouh ◽  
M.A. Sharaf ◽  
A.S. Saad
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Helium Burning

Laser microprobe fourier transform mass spectrometry. Preliminary results for feasibility and evaluation

1988 ◽  
Vol 2 (7) ◽  
pp. 146-150 ◽  
Author(s):  
M. Pelletier ◽  
G. Kreier ◽  
J. F. Muller ◽  
D. Weil ◽  
M. Johnston ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Fourier Transform ◽  
Fourier Transform Mass Spectrometry ◽  
Preliminary Results ◽  
Laser Microprobe
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