scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

scholarly journals Bright and dark 1– soliton solutions to perturbed Schrodinger – hirota equation with power law nonlinearity via semi – inverse variation method and ansatz method

2017 ◽  
Vol 5 (2) ◽  
pp. 39 ◽  
Author(s):  
S. Subhaschandra Singh
Keyword(s):  
Exact Solutions ◽  
Power Law ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Variation Method ◽  
Science And Engineering ◽  
Ansatz Method ◽  
Hirota Equation

This paper studies perturbed Schrodinger Hirota equation with power law nonlinearity by obtaining its 1 – soliton solutions via He’s semi – inverse variation method and the Ansatz method and the results reveal that these methods are very effective ones for obtaining exact solutions to various types of nonlinear evolution equations appearing in the studies of science and engineering.

The shock peakon wave solutions of the general Degasperis–Procesi equation

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Lijuan Qian ◽  
Raghda A. M. Attia ◽  
Yuyang Qiu ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Stability Property ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Different Types ◽  
The Stability

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the shallow water outflows. Some shock peakon wave solutions are obtained by using these methods. Moreover, some figures are sketched for these solutions to explain more physical properties of the general DP equation and to figure out the coincidence between different types of obtained solutions. The stability property by using the features of the Hamiltonian system is tested to some obtained solutions to show their ability for applying in the model’s applications. The obtained solutions were verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows their power and effectiveness for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method
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