Analytic solutions of the (2+1)-dimensional nonlinear evolution equations using the sine–cosine method

Taşcan, Filiz; Bekir, Ahmet

doi:10.1016/j.amc.2009.09.027

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Introduction2

The Bilinear Form and N-soliton Solutions1

H Kumar1

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2010

2024

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Cited by 46 publications

(21 citation statements)

References 33 publications

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“…Using the relation between binary Bell polynomials and standard Hirota bilinear operator [5,6], the Bellpolynomial expressions (21) can be cast into the bilinear form,…”

Section: The Bilinear Form and N-soliton Solutionsmentioning

confidence: 99%

Integrability of a (2+1)-dimensional generalized breaking soliton equation

2015

Applied Mathematics Letters

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“…Using the relation between binary Bell polynomials and standard Hirota bilinear operator [5,6], the Bellpolynomial expressions (21) can be cast into the bilinear form,…”

Section: The Bilinear Form and N-soliton Solutionsmentioning

confidence: 99%

Integrability of a (2+1)-dimensional generalized breaking soliton equation

2015

Applied Mathematics Letters

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“…In the present work we will extend our study to the two higher dimensional Boussinesq equations, namely, the (2 + 1)-dimensional Boussinesq equation [29,30,36,37]:…”

Section: H Kumarmentioning

confidence: 99%

Dynamics of Shallow Water Waves with Various Boussinesq Equations

Kumar¹,

Malik

Gautam

et al. 2017

Acta Phys. Pol. A

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Attempt has been made to construct the solitary waves and shock wave solutions or domain walls (in higher dimension) for various Boussinesq equations. The method of undetermined coefficients have been used to explore the exact analytical solitary waves and shock wave solutions in terms of bell-shaped sech p function and kinkshaped tanh p function for the considered equations. The Boussinesq equation in the (1 + 1)-dimensional, the (2 + 1)-dimensional and the (3 + 1)-dimensional equations are studied and the parametric constraint conditions and uniqueness in view of both solitary waves and shock wave solutions are determined. Such solutions can be valuable and desirable for explaining some nonlinear physical phenomena in nonlinear science described by the Boussinesq equations. The effect of the varying parameters on the development of solitary waves and shock wave solutions have been demonstrated by direct numerical simulation technique.

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“…Also, the explicit formulas may provide physical information and help us to understand the mechanism of related physical models. Recently, there have been a multitude of methods presented for solving Nonlinear partial differential equations (NPDEs), for instance, the tanh-method [1][2][3], the extended tanh method [4][5][6], the sine-cosine method [7][8][9], the homogeneous balance method [10], homotopy analysis method [11][12][13][14], the F −expansion method [15], three-wave method [16][17][18], extended homoclinic test approach [19,20], the ( [21] and the exp-function method [22][23][24].…”

Section: Introductionmentioning

confidence: 99%