Exact travelling solutions for some nonlinear physical models by ( G′/ G)-expansion method

Bahrami, B Salim; Abdollahzadeh, Hadi; Berijani, I M; Ganji, D.D.; Abdollahzadeh, M.

doi:10.1007/s12043-011-0100-9

Cited by 17 publications

(11 citation statements)

References 32 publications

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“…The two-dimensional sine-Gordon equation (8) and Dodd-Bullough-Mikhailov equation (9) have been widely applied in many fields such as solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on [7]. To look for the travelling wave solutions of eq.…”

Section: Applications To Physical Modelsmentioning

confidence: 99%

“…which describes various processes in dusty plasma, such as Langmuir, dust-acoustic wave and electromagnetic waves [7]. We suppose that eq.…”

Section: Applications To Physical Modelsmentioning

confidence: 99%

“…In particular, there has been considerable interest in seeking exact travelling wave solutions of nonlinear evolution equations that describe some important physical and dynamic processes. In the past several decades, many powerful methods such as variational iteration method [1], homotopy analysis method [2], homotopy perturbation technique [3], modified tanh-coth method [4], the Jacobi elliptic function method [5], (G /G)-expansion method [6][7][8], the expfunction method [9][10][11][12], trial equation method [13], spectral collocation method [14] and many other techniques were used to obtain exact travelling wave solutions of nonlinear problems. More precisely, there is no unified method that can be used to handle all types of nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, finding travelling wave solutions of nonlinear equations is of fundamental interest to understand the equations fully. In this paper, we shall find the exact travelling wave solutions for some nonlinear physical models and coupled equations such as Higgs equation, Maccari system and Schrödinger-KdV equation [6,7] by using the Kudryashov method. The computer symbolic systems such as Maple and Mathematica allow us to perform complicated and tedious calculations.…”

Section: Introductionmentioning

confidence: 99%

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Exact travelling wave solutions for some important nonlinear physical models

Lee

Sakthivel

2013

Pramana - J Phys

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The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrodinger-KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics. Abstract. The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger-KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.

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Section: Applications To Physical Modelsmentioning

confidence: 99%

“…which describes various processes in dusty plasma, such as Langmuir, dust-acoustic wave and electromagnetic waves [7]. We suppose that eq.…”

Section: Applications To Physical Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact travelling wave solutions for some important nonlinear physical models

Lee

Sakthivel

2013

Pramana - J Phys

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“…Consider the following. The application of the feature equations can be found in [13][14][15][16][17].…”

Section: The Second Type Exact Solutionmentioning

confidence: 99%

Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers

Jiang

Wang

Hua

2013

Advances in Optical Technologies

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With the increasing input power in optical fibers, the dispersion problem is becoming a severe restriction on wavelength division multiplexing (WDM). With the aid of solitons, in which the shape and speed can remain constant during propagation, it is expected that the transmission of nonlinear ultrashort pulses in optical fibers can effectively control the dispersion. The propagation of a nonlinear ultrashort laser pulse in an optical fiber, which fits the high-order nonlinear Schrödinger equation (NLSE), has been solved using the G /G expansion method. Group velocity dispersion, self-phase modulation, the fourth-order dispersion, and the fifth-order nonlinearity of the high-order NLSE were taken into consideration. A series of solutions has been obtained such as the solitary wave solutions of kink, inverse kink, the tangent trigonometric function, and the cotangent trigonometric function. The results have shown that the G /G expansion method is an effective way to obtain the exact solutions for the high-order NLSE, and it provides a theoretical basis for the transmission of ultrashort pulses in nonlinear optical fibers.

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Study on Analytical Solutions of K-dV Equation, Burgers Equation, and Schamel K-dV Equation with Different Methods

Mohanty

Dev

2021

Lecture Notes in Mechanical Engineering

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Exact travelling solutions for some nonlinear physical models by ( G′/ G)-expansion method

Cited by 17 publications

References 32 publications

Exact travelling wave solutions for some important nonlinear physical models

Exact travelling wave solutions for some important nonlinear physical models

Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers

Study on Analytical Solutions of K-dV Equation, Burgers Equation, and Schamel K-dV Equation with Different Methods

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