Traveling wave solutions by extended trial equation method

2013 ◽  
Author(s):  
Yusuf Gurefe ◽  
Emine Misirli
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Extended Trial

scholarly journals Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 742 ◽  
Author(s):  
Tao Liu
Keyword(s):  
Fractional Derivative ◽  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Singular Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Fifth Order ◽  
Fkdv Equation

We study a fifth order time-fractional KdV equation (FKdV) under meaning of the conformal fractional derivative. By trial equation method based on symmetry, we construct the abundant exact traveling wave solutions to the FKdV equation. These solutions show rich evolution patterns including solitons, rational singular solutions, periodic and double periodic solutions and so forth. In particular, under the concrete parameters, we give the representations of all these solutions.

scholarly journals On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

2017 ◽  
Vol 7 (3) ◽  
pp. 265-270
Author(s):  
Gülnur Yel ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Trigonometric Function ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this work, we construct the exact traveling wave solutions of the fractional (2+1)-dimensional Davey-Stewartson equation system (D-S) that is complex equation system using the Modified Trial Equation Method (MTEM). We obtained trigonometric function solutions by this method that are new in literature.

Optical solitons in DWDM system by extended trial equation method

Optik ◽  
2017 ◽  
Vol 141 ◽  
pp. 157-167 ◽  
Author(s):  
Mehmet Ekici ◽  
Abdullah Sonmezoglu ◽  
Qin Zhou ◽  
Anjan Biswas ◽  
Malik Zaka Ullah ◽  
...  
Keyword(s):  
Optical Solitons ◽  
Equation Method ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Dwdm System ◽  
Extended Trial

Optical solitons for paraxial wave equation in Kerr media

2019 ◽  
Vol 33 (03) ◽  
pp. 1950020 ◽  
Author(s):  
Kashif Ali ◽  
Syed Tahir Raza Rizvi ◽  
Badar Nawaz ◽  
Muhammad Younis
Keyword(s):  
Wave Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Equation Method ◽  
Kerr Media ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Paraxial Wave Equation ◽  
Extended Trial

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

Optical soliton perturbation for Gerdjikov–Ivanov equation by extended trial equation method

Optik ◽  
2018 ◽  
Vol 158 ◽  
pp. 747-752 ◽  
Author(s):  
Anjan Biswas ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu ◽  
Fayequa B. Majid ◽  
Houria Triki ◽  
...  
Keyword(s):  
Optical Soliton ◽  
Equation Method ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Soliton Perturbation ◽  
Extended Trial

Nematicons in liquid crystals by extended trial equation method

2017 ◽  
Vol 26 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Mehmet Ekici ◽  
Mohammad Mirzazadeh ◽  
Abdullah Sonmezoglu ◽  
Malik Zaka Ullah ◽  
Qin Zhou ◽  
...  
Keyword(s):  
Liquid Crystals ◽  
Shock Waves ◽  
Governing Equation ◽  
Plane Waves ◽  
Equation Method ◽  
Integration Algorithm ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
First Time ◽  
Extended Trial

This paper employs extended trial equation method to retrieve nematicons in liquid crystals from its governing equation. In addition, several other forms of solution naturally emerged from the integration algorithm. These are shock waves, singular solitons, snoidal waves, periodic singular waves, plane waves and others. These variety of solutions are being reported for the first time in the context of liquid crystals.

Extended Trial Equation Method for Nonlinear Partial Differential Equations

2015 ◽  
Vol 70 (4) ◽  
pp. 269-279 ◽  
Author(s):  
Khaled A. Gepreel ◽  
Taher A. Nofal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Equation Method ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
Partial Differential ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Extended Trial

AbstractThe main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber–Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

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