Exact solutions of the coupled Higgs equation and the Maccari system using He’s semi-inverse method and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math>-expansion method

Jabbari, Azizeh; Kheiri, Hossein; Bekir, Ahmet

doi:10.1016/j.camwa.2011.07.003

Cited by 75 publications

(23 citation statements)

References 24 publications

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“…Remark 1. By setting 𝜎 = 0, we get the similar solutions (73)-(74 ) of Maccari system (1-2) reported in [29,32].…”

Section: He's Semi-inverse Methodssupporting

confidence: 77%

“…\end{equation}$$Similarly, we can consider the following solutions

\begin{equation} \varphi (\eta )=A\text{sech}^{2}(B\eta ),\ \varphi (\eta )=A\coth (B\eta ), \text{ }\varphi (\eta )=A\tanh (B\eta )\ \text{and }\varphi (\eta )=A\text{ csch}(B\eta ), \end{equation}

to obtain wide variety of exact solutions of the SMS (). Remark By setting

\sigma =0

, we get the similar solutions ()–( ) of Maccari system () reported in [29, 32]. …”

Section: The Exact Solutions Of the Smssupporting

confidence: 77%

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Exact solutions of the stochastic Maccari system forced by multiplicative noise

et al. 2022

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In the Itô sense, we look at the stochastic Maccari system (SMS) with multiplicative noise. To generate new analytical stochastic solutions, we use three separate techniques including sine-cosine, Riccati-Bernoulli sub-ODE, and semi-inverse.Such solutions are critical for comprehending some fascinating and complex physical phenomena. In addition, some results from earlier studies are generalized. Furthermore, we investigate the impact of stochastic term on the exact solutions of the SMS.

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“…Remark 1. By setting 𝜎 = 0, we get the similar solutions (73)-(74 ) of Maccari system (1-2) reported in [29,32].…”

Section: He's Semi-inverse Methodssupporting

confidence: 77%

“…\end{equation}$$Similarly, we can consider the following solutions

\begin{equation} \varphi (\eta )=A\text{sech}^{2}(B\eta ),\ \varphi (\eta )=A\coth (B\eta ), \text{ }\varphi (\eta )=A\tanh (B\eta )\ \text{and }\varphi (\eta )=A\text{ csch}(B\eta ), \end{equation}

to obtain wide variety of exact solutions of the SMS (). Remark By setting

\sigma =0

, we get the similar solutions ()–( ) of Maccari system () reported in [29, 32]. …”

Section: The Exact Solutions Of the Smssupporting

confidence: 77%

Exact solutions of the stochastic Maccari system forced by multiplicative noise

et al. 2022

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“…We present He's semi-inverse method (HSIM) for the exact solution of nonlinear time fractional differential equations, built by Jabbari et al [49].…”

Section: He's Semi-inverse Methodsmentioning

confidence: 99%

The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta-Derivative

Özkan

2021

Axioms

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Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, He’s semi-inverse variation method and the ansatz method have been applied to find the soliton solutions for fractional Korteweg–de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by Atangana’s conformable derivative (beta-derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.

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“…There are many methods to study the exact traveling wave solutions of the nonlinear differential Equations, such as the inverse scattering method [1], Jacobi elliptic function expansion method [2], homogeneous balance method [3], ( ) G G ′ -expansion method [4], and so on. At the same time, Liu [5] introduced the complete discrimination system method to give the classification of exact traveling wave solutions to some nonlinear equations, the method is simple and efficient.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we focus on the Coupled-Higgs Equation to classify its traveling wave solutions. A. Jabbari et al [4] have got some traveling wave solutions to the Coupled-Higgs Equation. By Liu's method, we'll classify exact traveling wave solutions to the Coupled-Higgs Equation.…”

Section: Introductionmentioning

confidence: 99%