Partial Differential Equations and Solitary Waves Theory

Wazwaz, Abdul‐Majid

doi:10.1007/978-3-642-00251-9

Cited by 866 publications

(756 citation statements)

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“…Substituting (27) into (11), collecting the coe cients of cos i (ξ ), i = , , and equating each coe cient to zero we nd…”

Section: U(x Y Z T) = ± √ −Rs Coth (Kx + Ry + Sz + Krs T) (26)mentioning

confidence: 99%

“…In the open literature, a set of systematic methods have been developed to obtain explicit solutions for nonlinear (1+1) and (2+1)-dimensional equations. The resulting solutions involve generic phase shifts and wave frequencies containing many existing choices [9][10][11][12][13][14]. In the recent studies in this direction, physicists, engineers, and mathematicians mostly focus their studies on the (1+1)-dimensional, such as the Korteweg-de Vires (KdV), the modi ed Korteweg-de Vires (mKdV) equations, and the (2+1)-dimensional integrable models such as the Kadomtsev-Petviashivili (KP) and the Nizhnik-NovikovVeselov (NNV) equations.…”

Section: Introductionmentioning

confidence: 99%

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Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation

Wazwaz

2017

Open Engineering

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We present exact solutions for new (3+1)-dimensional nonlinear equations of wave propagation and uids. We use the tanh/sech method combined with a computer symbolic system for a reliable treatment of this work. We determine a variety of exact solutions for each equation that contains soliton, kink and periodic solutions. The constraints that guarantee the existence of soliton and kink solutions were examined and found to be related to the coe cients k, r and s of the space variables x, y, and z respectively.

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“…Substituting (27) into (11), collecting the coe cients of cos i (ξ ), i = , , and equating each coe cient to zero we nd…”

Section: U(x Y Z T) = ± √ −Rs Coth (Kx + Ry + Sz + Krs T) (26)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation

Wazwaz

2017

Open Engineering

Self Cite

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“…The components u n (x) of the solution u(x) will be determined recurrently, and Adomian polynomials can be constructed for various classes of nonlinearity according to specific algorithms presented by Wazwaz [9]. Substituting (14) and (15) into (13) yields…”

Section: E27mentioning

confidence: 99%

“…This method provides the solution in a rapidly convergent series solution and has been successfully applied to a wide class of boundary value problems [2,3,4,5,6,7,8,9,10]. The convergence of the decomposition series has been investigated by several researchers [11,12].…”

Section: Introductionmentioning

confidence: 99%

An approach for solving singular two point boundary value problems: analytical and numerical treatment

Chun¹,

Ebaid²,

Lee³

et al. 2012

ANZIAMJ

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The numerical treatment of two-point singular boundary value problems has always been a difficult and challenging task due to the singularity behaviour that occurs at a point. Various efficient numerical methods have been proposed to deal with such boundary value problems. We present a new efficient modification of the Adomian decomposition method for solving singular boundary value problems, both linear and nonlinear. Numerical examples illustrate the efficiency and accuracy of the proposed method.

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“…The linear advection equation is simple in form and yet it is one of the most difficult equations to solve accurately by numerical means [8]. This equation is challenging to solve as it causes some discontinuities with neither dispersion nor dissipation.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Two Spatial Discretization Schemes for Advection Equation

Bakodah¹

2016

IJMNTA

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In this paper, we describe a comparison of two spatial discretization schemes for the advection equation, namely the first finite difference method and the method of lines. The stability of the methods has been studied by Von Neumann method and with the matrix analysis. The methods are applied to a number of test problems to compare the accuracy and computational efficiency. We show that both discretization techniques approximate correctly solution of advection equation and compare their accuracy and performance.

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Partial Differential Equations and Solitary Waves Theory

Cited by 866 publications

References 0 publications

Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation

Exact Soliton and Kink Solutions for New (3+1)-Dimensional Nonlinear Modified Equations of Wave Propagation

An approach for solving singular two point boundary value problems: analytical and numerical treatment

A Comparative Study of Two Spatial Discretization Schemes for Advection Equation

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