New Exact Solutions of Ion-Acoustic Wave Equations by (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mi>G</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>/</mml:mo><mml:mi>G</mml:mi></mml:math>)-Expansion Method

Taha, Wafaa M.; Noorani, Mohd Salmi Md; Hashim, Ishak

doi:10.1155/2013/810729

Cited by 9 publications

(7 citation statements)

References 33 publications

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“…Eq.1 can be solved by using the (G ′ /G)-expansion method with different transformations [17]. To have a self consistent paper, we also give the solution of Eq.1 by using (G ′ /G)-expansion method with a transformation η = x − V p t. Balancing the terms ΨΨ ′′ and Ψ 4 in Eq.6, we get the positive balancing parameter m = 1.…”

Section: Exact Solutions Of the Schamel-kdv Equation By Using (G ′ /Gmentioning

confidence: 99%

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Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

Dönmez¹,

Dağhan²

2016

SDÜ Fen Bil Enst Der

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Abstract:The wave properties in a dusty space plasma consisting of positively and negatively charged dust as well as distributed nonisothermal electrons are investigated by using the exact traveling wave solutions of the Schamel-KdV equation. The analytic solutions are obtained by the different types (G ′ /G)-expansion methods and direct integration. The nonlinear dynamics of ion-acoustic waves for the various values of phase speed V p , plasma parameters α, σ , and σ d , and the source term µ are studied. We have observed different types of waves from the different analytic solutions obtained from the different methods. Consequently, we have found the discontinuity, shock or solitary waves. It is also concluded that these parameters play an important role in the presence of solitary waves inside the plasma. Depending on plasma parameters, the discontinuity wave turns into solitary wave solution for the certain values of the phase speed and plasma parameters. Additionally, exact solutions of the Schamel-KdV equation may also be used to understand the wave types and properties in the different plasma systems. Farklı Metodlar ile Schamel-KdV denkleminin Analitik Çözümleri: Tozlu Uzay Plazmasına UygulanmasıAnahtar Kelimeler Schamel-KdV denklemi, Tozlu uzay plazması, Sok dalgası, SolitonÖzet:İçerisinde negatif ve pozitif yüklü tozların yanında dagılmış izotermal olmayan elektronlar barındıran tozlu uzay plazmasındaki dalganın özellikleri, Schamel-KdV denklemlerinin tam ilerleyen dalga çözümleri kullanılarak incelenmiştir. Analitik çözümler, (G ′ /G)-genişleme methodunun farklı tipleri ve direk integrasyon kullanılarak bulunmuş-tur.İon-akustik dalgasının lineer olmayan dinamigi, faz hızının V p , plazma parametreleri α, σ , ve σ d , ve kaynak terimi µ'nun farklı degerleri için çalışılmıştır. Bunun sonucunda, farklı methodlardan elde edilen farklı analitik çözümler ile farklı türden dalgalar gözlemledik ve süreksiz,şok veya soliton dalgası bulduk. Aynı zamanda, yukarıda verilen parametrelerin plazma içerisinde soliton tipi dalgaların oluşmasında önemli bir rol oynadıgı sonucuna ulaşılmıştır. Bu parametrelere baglı olarak süreksiz dalga plazma parametrelerinin ve faz hızının belli degerleri için soliton tipi bir dalgaya donüşür. Bunlara ek olarak, Schamel-KdV denkleminin tam analitik çözümleri, verilen bir plazmanın özelliklerinin ve dalga tiplerinin anlaşılması için farklı plazma sistemlerine de uygulanabilir.

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Section: Exact Solutions Of the Schamel-kdv Equation By Using (G ′ /Gmentioning

confidence: 99%

“…Note that we reach to the Schamel equation when b = 0 [7,8] and the KdV equation when a = 0 [9,10]. Due to the various applications of Eqs.1 in the literature, many exact solutions of the Schamel-KdV equation have been obtained [3,[7][8][9][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

Dönmez¹,

Dağhan²

2016

SDÜ Fen Bil Enst Der

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“…For example, travailing wave variables in travelling wave solution of non-linear PDEs. numerous methods to find exact solution of nonlinear PDFs, have been suggested in the literature like: the tanh-coth method [1,2], sine-cosine method [3], homogeneous balance method [4,5], exp-function method [6], first-integral method [7], Jacobi elliptic function method [8], and (𝐺 ′ /𝐺)-Expansion method [9,10,11]. The standard method offered by Malfliet [12] is a strong technique to compute exact traveling waves solutions of non-linear partial differential equations, we will utilize the standard tanh method to find the traveling wave for a nonlinear diffusionconvection equation for different values of m and n [13,14,15].…”

Section: -Introductionmentioning

confidence: 99%

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Aziz¹,

Taha²,

Hameed³

et al. 2023

Tikrit J. Pure Sci.

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Exact solutions of traveling wave are acquired by employ a relatively new technique which is called standard tanh method for a nonlinear diffusion–convection equation. The tanh method is applied for the first time for finding travelling wave solutions for the nonlinear diffusion–convection equation , where n and m, are integers, and , of order (m=4, n=7) and (m=5, n=9). Analytical solutions of a nonlinear diffusion–convection equations are obtained as a polynomial in tanh(x), and the plots for exact solutions are given. The obtained results are compared with F-Expansion method to validate the proposed approach.

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“…For example, travailing wave variables in travelling wave solution of non-linear PDEs. numerous methods to find exact solution of nonlinear PDFs, have been suggested in the literature like: the tanh-coth method [1,2], sine-cosine method [3], homogeneous balance method [4,5], exp-function method [6], first-integral method [7], Jacobi elliptic function method [8], and ( ′ / )-Expansion method [9,10,11]. The standard method offered by Malfliet [12] is a strong technique to compute exact traveling waves solutions of non-linear partial differential equations, we will utilize the standard tanh method to find the traveling wave for a nonlinear diffusionconvection equation for different values of m and n [13,14,15].…”

Section: -Introductionmentioning

confidence: 99%

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

Aziz¹,

Taha²,

Hameed³

et al. 2018

Tikrit J. Pure Sci.

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Exact solutions of traveling wave are acquired by employ a relatively new technique which is called standard tanh method for a nonlinear diffusion-convection equation. The tanh method is applied for the first time for finding travelling wave solutions for the nonlinear diffusionconvection equation = ( ) + ( ) , where n and m, are integers, and ≥ > 1, of order (m=4, n=7) and (m=5, n=9). Analytical solutions of a nonlinear diffusion-convection equations are obtained as a polynomial in tanh(x), and the plots for exact solutions are given. The obtained results are compared with F-Expansion method to validate the proposed approach.

show abstract

New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G)-Expansion Method

Cited by 9 publications

References 33 publications

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

Analytic Solutions of the Schamel-KdV Equation by Using Different Methods: Application to a Dusty Space Plasma

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

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