Analytical Solutions for Nonlinear Dispersive Physical Model

Ma, Wen‐Xiu; Ali, Mohamed R.; Sadat, R.

doi:10.1155/2020/3714832

Cited by 15 publications

(10 citation statements)

References 34 publications

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“…Many other evolution equations such as time-fractional Benjamin-Bona Mahony equation (TFBBM) [17], (3 + 1)-dimensional extended date-Jimbo-Kashiwara-Miwa equation [18], Bruta-Gelfand equation [19], and similar boundary value problems arising from an adiabatic tubular chemical reactor theory [20], nuclear physics [21], and magneto-hydrodynamics incompressible nanofluid flow past over an infinite rotating disk [22] have been solved using different analytical and numerical approaches [17] applied the integrating factor property to obtain analytical solution of TFBBM equation after reducing the equation to nonlinear fractional ordinary differential equation using its Lie symmetry. In [18], a new exact Lump-soliton solution that localized in all spatio-temporal directions was derived using Hirota method.…”

Section: Original Research Articlementioning

confidence: 99%

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nchejane

Gbenro²

2022

JAMCS

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The nonlinear Schrödinger equation in one-dimensional coordinate is investigated numerically by employing explicit and implicit finite difference methods. It is shown that the explicit method is conditionally stable, and the condition for stability, which is a function of the time step and spatial step size, or several grid points are obtained. It is also shown that the implicit scheme is unconditionally stable and results in a tridiagonal matrix at each time level as a function of the nonlinear term. The effects of dispersion and nonlinearity concerning the time and space steps are also investigated. The validity of our scheme is established by reproducing some existing results on the constant-coefficient nonlinear Schrödinger equation. The schemes are then extended to study the variable coefficient equation, which has a growing interest and applications in many areas of nonlinear science.

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Section: Original Research Articlementioning

confidence: 99%

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nchejane

Gbenro²

2022

JAMCS

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“…In this paper, we study the VCBK equation, based on the associated Lie algebra [3,5,10,[19][20][21][22][23]. Eq.…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

Ali¹

2022

EAJAM

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We present Lie symmetry analysis to explore solitary wave solutions, twosoliton type solutions and three-soliton type solutions in variable-coefficient nonlinear physical phenomena. An example is a (2+1)-dimensional variable-coefficient Bogoyavlensky-Konopelchenko (VCBK) equation. We compute the Lie algebra of infinitesimals of its symmetry vector fields and an optimal system of one-dimensional sub-Lie algebras of the resulting symmetries. Two stages of Lie symmetry reductions will be built to reduce the VCBK equation to nonlinear ordinary differential equations (ODEs) and new analytical solutions to those ODEs will be found by using the integration method. Some of such resulting solutions to the VCBK equation and their dynamics will be illustrated through three-dimensional plots.

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“…G′/G expansion method has been implemented to investigate the exact solution of time fractional model of BBM-Burger equation in [24]. The authors in [25] utilized Lie symmetry approach to develop solution of fractional BBM equation. New soliton solutions for ð3 + 1Þ -dimensional Extended Date-Jimbo-Kashiwara-Miwa Equation has been established by means of Hirota method together with quadratic test functions in [26].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

Kamran

Abbas

Majeed

et al. 2022

Journal of Function Spaces

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The unidirectional propagation of long waves in certain nonlinear dispersive system is explained by the Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The purpose of this study is to investigate the BBM-Burger equation numerically using Caputo derivative and B-spline basis functions. The fractional derivative is considered in Caputo form, and L 1 formula is used for discretization of temporal derivative. The interpolation of space derivative is done with the help of B-spline functions. The effect of α and time on solution profile of travelling wave for different domain of x is discussed in this paper. The numerical results have been presented to show that the cubic B-spline method is effective and efficient in solving the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. Moreover, the convergence and stability of the proposed scheme are analyzed. The error norms are also calculated to check the accuracy of the proposed scheme. The numerical results reflect that the proposed scheme can be used for linear and highly nonlinear models.

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Analytical Solutions for Nonlinear Dispersive Physical Model

Cited by 15 publications

References 34 publications

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Nonlinear Schrodinger Equations with Variable Coefficients: Numerical Integration

Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

Numerical Simulation of Time Fractional BBM-Burger Equation Using Cubic B-Spline Functions

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