Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the -expansion method

Hubert, Malwe Boudoue; Betchewe, Gambo; Doka, Serge Y.; Crépin, Kofané Timoléon

doi:10.1016/j.amc.2014.04.065

Cited by 28 publications

(15 citation statements)

References 35 publications

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“…They are new exact solutions of Equation (6). Our method contains all the results mentioned by the G'/G method [19], the improved sub-ODE method [20] and auxiliary equation technique [21], etc., which were discussed in [22]. …”

Section: Remarkmentioning

confidence: 99%

New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation

Hong

2016

MCA

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Abstract:In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances, some of these solutions are degenerated to soliton-like solutions and trigonometric function solutions in the limit cases when the modulus of the Jacobi elliptic function solutions tends to 0 and 1, which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of higher-dimensional nonlinear partial differential equations in mathematical physics.

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Section: Remarkmentioning

confidence: 99%

New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation

Hong

2016

MCA

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“…. , ) are constants to be determined later with 2 + 2 ̸ = 0 and where the functions = ( ) and = ( ) are implicitly associated with (13) using the relations in (14).…”

Section: The ( / 1/ )-Expansionmentioning

confidence: 99%

“…Over the last few decades, exact solutions, analytical approximate solutions, and numerical solutions of NPDEs have been successfully obtained. The methods for obtaining exact explicit solutions of NPDEs are, for example, the ( / )-expansion method [6], the tanhfunction method [7,8], the exp-function method [9,10], the -expansion method [11], Hirota's direct method [12,13], Kudryashov method [14,15], and so on. Examples of the methods for obtaining analytical approximate solutions to NPDEs are the variational iteration method [16,17] (VIM), the Adomian decomposition method [18,19] (ADM), and the homotopy perturbation method [20,21] (HPM).…”

Section: Introductionmentioning

confidence: 99%

Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

Sirisubtawee

Koonprasert

Khaopant

et al. 2017

Mathematical Problems in Engineering

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We investigate methods for obtaining exact solutions of the (3 + 1)-dimensional nonlinear space-time fractional Jimbo-Miwa equation in the sense of the modified Riemann-Liouville derivative. The methods employed to analytically solve the equation are the ( / , 1/ )-expansion method and the novel ( / )-expansion method. To the best of our knowledge, there are no researchers who have applied these methods to obtain exact solutions of the equation. The application of the methods is simple, elegant, efficient, and trustworthy. In particular, applying the novel ( / )-expansion method to the equation, we obtain more exact solutions than using other existing methods such as the ( / )-expansion method and the exp(−Φ( ))-expansion method. The exact solutions of the equation, obtained using the two methods, can be categorized in terms of hyperbolic, trigonometric, and rational functions. Some of the results obtained by the two methods are new and reported here for the first time. In addition, the obtained exact explicit solutions of the equation characterize many physical meanings such as soliton solitary wave solutions, periodic wave solutions, and singular multiple-soliton solutions.

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“…Nonlinear electrical transmission lines are discrete systems but approximate the continuum systems quite well. By applying the Kirchhoff's laws and the continuum approximation to a nonlinear electrical line, Hubert et al [38] derived an equation of wave propagation and solved it via the Kudryashov method and the (G ′ /G)-expansion method which provided kink, antikink, and breather soliton solutions. Sardar et al [39] found multiple traveling wave solutions using three integration schemes (extended tanh method, (G ′ /G)-expansion method and sine-cosine method) to integrate the model of electrical transmission line.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

Aslan¹

2016

Commun. Theor. Phys.

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Soliton wave solutions for the nonlinear transmission line using the Kudryashov method and the -expansion method

Cited by 28 publications

References 35 publications

New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation

New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation

Two Reliable Methods for Solving the (3 + 1)‐Dimensional Space‐Time Fractional Jimbo‐Miwa Equation

Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

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