The exp&amp;lt;span style=&amp;quot;font-family:Symbol;font-size:11pt;&amp;quot;&amp;gt;(-j(x))&amp;lt;/span&amp;gt; Method and Its Applications for Solving Some Nonlinear Evolution Equations in Mathematical Physics

Shehata, Maha S. M.

doi:10.4236/ajcm.2015.54041

Cited by 9 publications

(3 citation statements)

References 29 publications

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“…Finally, n denotes the generalized full nonlinearity. Recently, many approaches have resulted in the exact solutions to NLPDEs which are mostly demonstrated through [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. One of the most famous and powerful ansatz methods which is described briefly and results in the closed form optical solutions for the NLPDEs is the MSEM.…”

Section: Introductionmentioning

confidence: 99%

Impressive and accurate solutions to the generalized Fokas-Lenells model

Bekir¹,

Zahran

Davodi

2022

Rev. Mex. Fís.

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In this article, we utilize the generalized full nonlinearity perturbed complex Fokas-Lenells model (GFLM) which is a general dynamics representation of modern electronic communications "Internet blogs, Facebook communication and Twitter comments". The modified simple equation method (MSEM) has been applied effectively to generate closed form solution. On the other hand, the Riccati-Bernoulli Sub-ODE method (RPSOM) which reduces the steps of calculation has been applied perfectly to achieve accurate solution to this equation. We established the solutions achieved by these distinct manners in same vein and parallel.

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Section: Introductionmentioning

confidence: 99%

Impressive and accurate solutions to the generalized Fokas-Lenells model

Bekir¹,

Zahran

Davodi

2022

Rev. Mex. Fís.

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“…Many trails have been penned for the physical problems in the last years to get the analytical solutions of the NLPDEs with the recent computer technology [1][2][3][4][5][6][7][8][9][10][11][12]. A variety of powerful methods have been developed such as the exp(−φ(ζ))expansion expansion method [13,14], the (G /G)-expansion method [15,16], the new extended direct algebraic method [17,18], the first integral method [19,20], the extended Jacobi elliptic function expansion method [21,22], and so on [23][24][25][26][27][28][29][30]. Furthermore, the current analysis concentrates over one such nonlinear evolution equation, known as the GI equation [31].…”

Section: Introductionmentioning

confidence: 99%

Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques

Shehata¹,

Rezazadeh²,

Jawad³

et al. 2021

Rev. Mex. Fís.

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In this article the perturbed Gerdjikov-Ivanov (GI)-equation which acts for the dynamics of propagation of solitons is employed. The balanced modified extended tanh-function and the non-balanced Riccati-Bernoulli Sub-ODE methods are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accuracy interpretation of the propagation of solitons. We held a comparison between our results and those are in the previous work. The efficiency of these methods for constructing the exact solutions has been demonstrated. It is shown that these different technique's reduces the large volume of calculations.

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“…Many methods are constructed by different authors through distinct published articles to demonstrate the solitary solutions for the NLPDE arising in different branches of science. Some of these methods are the well-known ansatze approaches methods, the majorities from which are building on the balance rule in its preparing except for the Riccati-Bernoulli Sub-ODE method and all listed [1][2][3][4][5][6][7][8][9][10][11][12][13], Most of the achieved solutions according to these methods are analogous to that obtained using the reduction methods and the Lie-semi-group methods.…”

Section: Introductionmentioning

confidence: 99%

Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation

Bekir

Shehata

Zahran

2021

Numerical Methods Partial

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In this article, we employ the Mikhailov–Novikov–Wang integrable equation (MNWIE) appearing by means of the perturbatives symmetry approach to the rating of integrable non‐evolutionary PDEs. The new exact soliton solutions of this equation which were not achieved before have been realized for the first time in the framework of the (G′/G)‐expansion method. In the same vein and parallel, the corresponding numerical solutions of this equation have been established using the variational iteration method (VIM).

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The exp<span style="font-family:Symbol;font-size:11pt;">(-j(x))</span> Method and Its Applications for Solving Some Nonlinear Evolution Equations in Mathematical Physics

Cited by 9 publications

References 29 publications

Impressive and accurate solutions to the generalized Fokas-Lenells model

Impressive and accurate solutions to the generalized Fokas-Lenells model

Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques

Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation

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