Analytical Solutions of (1+1)- Dimensional Distributed Long Wave (Dlw) Equation With Auxiliary Equation Method

GÖKTAŞ, Ahmet Mücahid; Yilmaz, Koray; Taşbozan, Orkun

doi:10.33773/jum.1089362

Journal of Universal Mathematics

2022

DOI: 10.33773/jum.1089362

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Analytical Solutions of (1+1)- Dimensional Distributed Long Wave (Dlw) Equation With Auxiliary Equation Method

Ahmet Mücahid GÖKTAŞ

Koray Yilmaz

Orkun Taşbozan

Abstract: In this article, the exact solutions of the (1+1)-dimensional (DLW) equation, a fractional partial differential equation in conformable sense, which is a nonlinear, are given. Furthermore, with the aid of the mathematica program it is seen that the analytical solutions revealed with the auxiliary equation method satisfies the equation.

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2024

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Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

Şahinkaya,

Kurt,

Yalçınkaya

2024

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The main purpose of the paper is obtaining the analytical results for beta fractional Caudrey–Dodd–Gibbon equation which is used to resolve complex problems in fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics by using auxiliary method. Beta derivative is a useful fractional operator due to satisfying basic properties of integer order derivative and also, allows us using chain rule and wave transform to turn nonlinear fractional partial differential equations into integer order ordinary differential equations. By the way many analytical methods can be applied to these equations. In order to understand the physical features of the solutions, 3D and 2D graphical illustrations are given. Finally, authors expect that the obtained solutions may give a deep insight for the explanation of physical phenomena in the fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics.

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Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

Şahinkaya,

Kurt,

Yalçınkaya

2024

Opt Quant Electron

View full text Add to dashboard Cite

show abstract

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Analytical Solutions of (1+1)- Dimensional Distributed Long Wave (Dlw) Equation With Auxiliary Equation Method

Cited by 1 publication

References 13 publications

Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

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