Traveling wave solutions of a (2 + 1)-dimensional Zakharov-like equation by the first integral method and the tanh method

Darvishi, M. T.; Arbabi, Somayeh; Najafi, Mohammad; Wazwaz, Abdul‐Majid

doi:10.1016/j.ijleo.2016.04.033

Cited by 36 publications

(12 citation statements)

References 20 publications

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“…G -expansion method [9][10][11], the Clarkson-Kruskal (CK) direct method [12], the modified Kudryashov method [13], adomian decomposition methods [14][15][16], [17], first integral method [18], collocation method [19], new sub equation method [20], residual power series method [21], homogeneous balance method [22] and so on [28][29][30][31][32][33][34][35][36][37]. Consider the KPP equation [23] where v,  and  are real numbers.…”

Section: 'mentioning

confidence: 99%

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

Durur

Yokuş

2020

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In the current study, analytical solutions are constructed by applying (1 / ) G -expansion method to the Kolmogorov-Petrovskii-Piskunov (KPP) equation. Hyperbolic type exact solutions of the KPP equation are presented with the successfully applied method. 3D, 2D and contour graphics are presented by giving special values to the parameters in the solutions obtained. This article explores the applicability and effectiveness of this method on nonlinear evolution equations (NLEEs).

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Section: 'mentioning

confidence: 99%

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

Durur

Yokuş

2020

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…)-expansion method [4], Clarkson-Kruskal (CK) direct method [5], improved tan ( )/2-expansion method [6], Sumudu transform method [7], new expansion method [8], extended sinh-Gordon equation expansion method [9], the modified Kudryashov method [10], (1/ ′)-expansion method [11][12][13][14][15], collocation method [16,17], first integral method [18], F-expansion method [19], the modified exponential function method [20], Difference scheme method [21] and so on [22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

(G'/G,1/G)-expansion method for analytical solutions of Jimbo-Miwa equation

Yokuş¹,

Durur²

2021

Cumhuriyet Science Journal

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The main goal of this study is obtaining analytical solutions for (3+1)-dimensional Jimbo-Miwa Equation which the second equation in the well-known KP hierarchy of integrable systems. For the (3+1DJM) equation, hyperbolic, trigonometric, complex trigonometric and rational traveling wave solutions have been constructed by applying the ( ′/ , 1/ )expansion method. Then, real and imaginary graphics are presented by giving special values to the constants in the solutions obtained. These graphics are a special solution of the (3+1DJM) equation and represent a stationary wave of the equation. The ( ′/ , 1/ )expansion method is an effective and powerful method for solving nonlinear evolution equations (NLEEs). Ready computer package program is used to obtain the solutions and graphics presented in this study.

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“…(1 / ) G -expansion method [6][7][8][9] the Clarkson-Kruskal direct method [10], the auto-Bäcklund transformation method [11], decomposition method [12], homogeneous balance method [13], the first integral method [14], residual power series method [15], collocation method [16], modified Kudryashov method [17], sine-Gordon expansion method [18,19], the improved Bernoulli sub-equation function method, [20] and so on [21][22][23][30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the Benney–Luke equation via (1/G')-expansion method

Durur

Yokuş

2021

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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In this study, the (1 / ) G -expansion method was implemented to solve the Benney-Luke (BL) equation. Exact solutions of the BL equation were obtained via this method. The solutions obtained from the BL equation were in hyperbolic form. 3D, 2D and contour graphs of obtained solutions are presented. Results show that the (1 / ) Gexpansion method provides an efficient and straightforward mathematical instrument for finding solutions of nonlinear evolution equations (NLEEs).

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Traveling wave solutions of a (2 + 1)-dimensional Zakharov-like equation by the first integral method and the tanh method

Cited by 36 publications

References 20 publications

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

(G'/G,1/G)-expansion method for analytical solutions of Jimbo-Miwa equation

Exact solutions of the Benney–Luke equation via (1/G')-expansion method

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