Traveling Wave Solutions of the Nonlinear (3 + 1)‐Dimensional Kadomtsev‐Petviashvili Equation Using the Two Variables (G′/G, 1/G)‐Expansion Method

Zayed, Elsayed M.E.; Ibrahim, Safaa A.; Abdelaziz, Mahmoud A. M.

doi:10.1155/2012/560531

Cited by 35 publications

(18 citation statements)

References 32 publications

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“…As a pioneer work Li et al [15] has applied the two-variable (G ′ /G, 1/G)-expansion method and found the exact solutions of Zakharov equations. Some applications of the (G ′ /G, 1/G)-expansion method can be seen in [16,17,18,19,20]. (1/G ′ )-expansion method introduced by Yokus [21] firstly.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for two different non-linear partial differential equations

Dağhan¹,

Esen²

2018

ntmsci

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Travelling wave solutions of the Drinfeld-Sokolov system and Modified Benjamin-Bona-Mahony equations are studied analytically by using two dependent (G ′ /G, 1/G) and (1/G ′)-expansion methods. Solutions are obtained with different forms of functions as hyperbolic, trigonometric and rational functions. These methods are really effective methods, and can be simply applicable to the nonlinear evolution equations encountered in the different physical systems.

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Section: Introductionmentioning

confidence: 99%

Exact solutions for two different non-linear partial differential equations

Dağhan¹,

Esen²

2018

ntmsci

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“…As a pioneer work, twovariable (G ′ /G, 1/G)-expansion method was explained and applied to Zakharov equation in [22]. There are several studies related to this generalized method to obtain the traveling wave solutions of the some nonlinear differential equations [10,20,[23][24][25][26]. Hence it would be interesting to obtain the different forms of the traveling wave solutions of the Schamel-KdV equation.…”

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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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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“…Nonlinear wave phenomena appear in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, biology, solid state physics, chemical kinematics, chemical physics, and geochemistry. To obtain traveling wave solutions, many powerful methods have been presented, such as the inverse scattering method [1], the tanh-function method [2][3][4][5][6][7][8], the Hirota bilinear transform method [9], the truncated Painleve expansion method [10][11][12][13], the Backlund transform method [14,15], the Exp-function method [16][17][18][19][20], the Jacobi elliptic function expansion method [21][22][23], the generalized Riccati equations method [24][25][26], the ( / )expansion method [27][28][29][30][31][32][33], and the ( / , 1/ )-expansion method [34][35][36]. Conte and Musette [37] presented an indirect method to seek more solitary wave solutions of some NPDEs that can be expressed as polynomials in two elementary functions which satisfy a projective Riccati equation [38].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics

Zayed

Alurrfi

2014

Abstract and Applied Analysis

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We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.

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Traveling Wave Solutions of the Nonlinear (3 + 1)‐Dimensional Kadomtsev‐Petviashvili Equation Using the Two Variables (G^′/G, 1/G)‐Expansion Method

Cited by 35 publications

References 32 publications

Exact solutions for two different non-linear partial differential equations

Exact solutions for two different non-linear partial differential equations

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

The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics

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