Domain walls to Boussinesq-type equations in (2 + 1)-dimensions

Triki, Houria; Kara, A. H.; Biswas, Anjan

doi:10.1007/s12648-014-0466-x

Cited by 17 publications

(6 citation statements)

References 32 publications

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“…There is no justification to (9), but here no matter as we are only concerned with extending an equation of dimension [(m − 1) + 1] to (m + 1) which is also based on the fact that this extension is not unique. Thus, we arrive to the result that the works here and in [21] are different.…”

Section: Indirect Extension and Formulation Of The Methodsmentioning

confidence: 99%

“…Solvability of these coupled equations occupies a wide area in the literature [18,19], and they are studied by using a variety of methods [2][3][4][5][6][7][8][9][10][11][12][13]. A class of higher-order nonlinear wave equations, among the KdV6 equation [20], are studied to inspect completely integrability.…”

Section: A Pde Is Completely Solvable For Rational Solutionsmentioning

confidence: 99%

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On the “ $${\hat{\varvec{kp}}}$$ k p ^ -operator”, new extension of the KdV6 to (m + 1)-dimensional equation and traveling waves solutions

Abdel‐Gawad

2016

Nonlinear Dyn

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Very recently, the KdV6 was extended to a (2 + 1)-dimensional equation by a direct way. Here, by using the "kp-operator" the extension of that equation is done in a rigorous mathematical formulation. Polynomial solutions to the closed form equation are obtained via the unified method. It is found that via nonlinear interactions of traveling waves the solutions of the constructed equation may not be unique. Also, these solutions may show solitary or explosive shock waves.

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Section: Indirect Extension and Formulation Of The Methodsmentioning

confidence: 99%

Section: A Pde Is Completely Solvable For Rational Solutionsmentioning

confidence: 99%

On the “ $${\hat{\varvec{kp}}}$$ k p ^ -operator”, new extension of the KdV6 to (m + 1)-dimensional equation and traveling waves solutions

Abdel‐Gawad

2016

Nonlinear Dyn

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“…It is also an important nonlinear model arising in physics, hydromechanics, and optics. It can also be used to describe a series of physical aspects about the spread of wave in plasma and nonlinear wave [61][62][63][64][65]. By applying the traveling wave transformation (8) to this equation and integrating it twice, and then setting the constants of integration equal to zero, it can be turned into a nonlinear ODE f…”

Section: Conformable Time-fractional Boussinesq Equationmentioning

confidence: 99%

Solitary Wave Solutions of Nonlinear Conformable Time-Fractional Boussinesq Equations

2019

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In this paper, the (G G)-expansion method based on conformable fractional derivative is proposed to solve time fractional partial differential equations in mathematical physics. To illustrate the validity of this method, we solve the Boussinesq equation, coupled time-fractional Boussinesq equations and a variety of exact solutions for them are successfully established. With the help of Maple software, three-dimensional solution graphs are presented.

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“…In order to find the solitary wave solution for Eq. (4), we practice the following solitary wave form [14][15][16][17][18][19][20][21][22][23][24] q(x, t) = A sech…”

Section: The Solitary Wave Solutionmentioning

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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Domain walls to Boussinesq-type equations in (2 + 1)-dimensions

Cited by 17 publications

References 32 publications

On the “ $${\hat{\varvec{kp}}}$$ k p ^ -operator”, new extension of the KdV6 to (m + 1)-dimensional equation and traveling waves solutions

On the “ $${\hat{\varvec{kp}}}$$ k p ^ -operator”, new extension of the KdV6 to (m + 1)-dimensional equation and traveling waves solutions

Solitary Wave Solutions of Nonlinear Conformable Time-Fractional Boussinesq Equations

Dynamics of Shallow Water Waves with Various Boussinesq Equations

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