A study on the compatibility of the generalized Kudryashov method to determine wave solutions

This paper extracts the analytical soliton solutions of the perturbed NLSE given in (1). We use successfully two integration methods namely the extended simple equation method and generalized Kudryashov method. In view of the results obtained, some new additional ones have been obtained. The results are dark, bright and exact solutions that propagate in the fiber optic and left-handed metamaterials (LHMs).

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Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method

Open Physics ◽

10.1515/phys-2018-0057 ◽

2018 ◽

Vol 16 (1) ◽

pp. 419-426 ◽

Cited By ~ 3

Author(s):

Rodica Cimpoiasu ◽

Alina Streche Pauna

Keyword(s):

Elliptic Functions ◽

Rational Functions ◽

Periodic Wave ◽

Equation Method ◽

Resonance Model ◽

Trial Equation Method ◽

Wave Solutions ◽

Generalized Kudryashov Method ◽

Wave Resonance ◽

Kudryashov Method

Abstract In this paper the nonlinear long-short (LS) wave resonance model is analyzed through a new perspective. We obtain the classification of exact solutions by making use of the complete discrimination system for the trial equation method and through the generalized Kudryashov method. These methods do generate complementary wave solutions such as bright and dark solitons, rational functions, Jacobi elliptic functions as well as singular and periodic wave solutions. Some among them extend the already reported solutions through other techniques. For some types of solutions adequately graphical representations are displayed. The concerned methods could also be used in order to study other interesting nonlinear evolution processes in n dimensions.

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SOLITARY WAVE SOLUTIONS FOR SPACE-TIME FRACTIONAL COUPLED INTEGRABLE DISPERSIONLESS SYSTEM VIA GENERALIZED KUDRYASHOV METHOD

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2005439g ◽

2021 ◽

pp. 1439

Author(s):

Ahmed Gaber ◽

Hijaz Ahmad

Keyword(s):

Solitary Wave ◽

Fractional Derivative ◽

Exact Solutions ◽

Space Time ◽

Solitary Wave Solutions ◽

Numerical Tests ◽

Wave Solutions ◽

Generalized Kudryashov Method ◽

Kudryashov Method ◽

Fractional System

In this article, space-time fractional coupled integrable dispersionless system is considered, and we use fractional derivative in the sense of modified Riemann-Liouville. The fractional system has reduced to an ordinary differential system by fractional transformation and the generalized Kudryashov method is applied to obtain exact solutions. We also testify performance as well as precision of the applied method by means of numerical tests for obtaining solutions. The obtained results have been graphically presented to show the properties of the solutions.

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SOLITARY WAVE SOLUTIONS OF SPACE TIME FDES USING THE GENERALIZED KUDRYASHOV METHOD

Acta Universitatis Apulensis ◽

10.17114/j.aua.2015.42.03 ◽

2015 ◽

Vol 42 ◽

Keyword(s):

Solitary Wave ◽

Space Time ◽

Solitary Wave Solutions ◽

Wave Solutions ◽

Generalized Kudryashov Method ◽

Kudryashov Method

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Harmonizing wave solutions to the Fokas-Lenells model through the generalized Kudryashov method

Optik ◽

10.1016/j.ijleo.2021.166294 ◽

2021 ◽

Vol 229 ◽

pp. 166294

Author(s):

Hemonta Kumar Barman ◽

Ripan Roy ◽

Forhad Mahmud ◽

M. Ali Akbar ◽

M.S. Osman

Keyword(s):

Wave Solutions ◽

Generalized Kudryashov Method ◽

Kudryashov Method

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

International Journal of Modern Physics B ◽

10.1142/s021797921950351x ◽

2019 ◽

Vol 33 (29) ◽

pp. 1950351 ◽

Cited By ~ 8

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.

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Research on sensitivity analysis and traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation via three different techniques

Physica Scripta ◽

10.1088/1402-4896/ac42eb ◽

2021 ◽

Author(s):

Melike Kaplan Yalçın ◽

Arzu Akbulut ◽

Nauman Raza

Keyword(s):

Sensitivity Analysis ◽

Nonlinear Equation ◽

Traveling Wave ◽

Function Method ◽

Graphical Representation ◽

Traveling Wave Solutions ◽

Analytical Techniques ◽

Wave Solutions ◽

Generalized Kudryashov Method ◽

Kudryashov Method

Abstract In the current manuscript, (4+1) dimensional Fokas nonlinear equation is considered to obtain traveling wave solutions. Three renowned analytical techniques, namely the generalized Kudryashov method (GKM), the modified extended tanh technique, exponential rational function method (ERFM) are applied to analyze the considered model. Distinct structures of solutions are successfully obtained. The graphical representation of the acquired results is displayed to demonstrate the behavior of dynamics of nonlinear Fokas equation. Finally, the proposed equation is subjected to a sensitive analysis.

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