Travelling Wave Solutions for the KdV‐Burgers‐Kuramoto and  Nonlinear Schrödinger Equations Which  Describe Pseudospherical Surfaces

Sayed, S. M.; Elhamahmy, Osman O.; Gharib, G. M.

doi:10.1155/2008/576783

Cited by 17 publications

(13 citation statements)

References 34 publications

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“…One notices that, from equation (10) 3.1.1. First family; case: b ¹ 0, and c ¹ 0 From equations (11), (12) and (13)…”

Section: The Bogning-djeumen Tchaho-kofané Methods (Bdkm)mentioning

confidence: 99%

“…Thus, the human being in general and the physicist in particular model the dynamics of nonlinear phenomena by mathematical equations of all outputs, among which are the nonlinear differential equations. They vary most often according to the physical system studied [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. If one thing is to get these equations, in order to analyze and understand the dynamics of these physical systems, another thing is to solve them and get solutions that are closer to reality.…”

Section: Introductionmentioning

confidence: 99%

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Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

Tchaho¹,

Omanda²,

Mbourou

et al. 2019

J. Phys. Commun.

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This work is dedicated to the construction of solitary wave solutions of the KdV-Burgers-Kuramoto equation. The peculiarity of the solutions obtained for this purpose is that they result from the combination of solitary waves of the bright and dark type thus generating multi-form solutions which are also called hybrid solitary waves. The Bogning-Djeumen Tchaho-Kofané method is used to obtain the results. The reliability and feasibility of these results are tested using numerical simulations.

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“…One notices that, from equation (10) 3.1.1. First family; case: b ¹ 0, and c ¹ 0 From equations (11), (12) and (13)…”

Section: The Bogning-djeumen Tchaho-kofané Methods (Bdkm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

Tchaho¹,

Omanda²,

Mbourou

et al. 2019

J. Phys. Commun.

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“…Now we describe the sine -cosine method [19], for a given nonlinear evolution equation, say, in two variables [25][26][27][28][29][30],…”

Section: The Sine -Cosine Methodsmentioning

confidence: 99%

Traveling wave solutions for a generalized Kawahara and Hunter-Saxton equations

Alali¹

2013

ijma

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Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the tanh-method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave variable is of first order, the equation reduces to the KdV equation with only a cubic dispersion term, while for the KE which includes a fifth order dispersion term the polynomial ansatz must necessary be of quadratic type. By solving the elliptic equation with coefficients that depend on the boundary conditions, velocity of the traveling waves, nonlinear strength, and dispersion coefficients, in the case of KdV equation we find the well-known solitary waves (solitons) for zero boundary conditions, as well as wave-trains of cnoidal waves for nonzero boundary conditions. Both solutions are either compressive (bright) or rarefactive (dark), and either propagate to the left or right with arbitrary velocity. In the case of KE with nonzero boundary conditions and zero cubic dispersion, we obtain cnoidal wave-trains which represent solutions to the TL equation. For KE with zero boundary conditions and all the dispersion terms present, we obtain again solitary waves, while for KE with all coefficients present and nonzero boundary condition, the solutions are written in terms of Weierstrass elliptic functions. For all cases of the KE we only find bright waves that are propagating to the right with velocity that is a function of both dispersion coefficients.

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“…x 32 1 2 and bg ¹ 0, then 15 1168 tanh 4 cosh 5 tanh 3 , 3 22 1 where the a i are constants and e = 1. Also, SAYED et al in [18] obtained some other traveling wave solutions as:…”

Section: Traveling Wave Solutions Of Kdv-burgers -Kuramoto (Kbk) Equamentioning

confidence: 99%

Some exact solutions of KdV-Burgers-Kuramoto equation

Alimirzaluo

Nadjafikhah

2019

J. Phys. Commun.

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Some exact solutions of KdV-Burgers-Kuramoto (KBK) equation are derived by the anzas and tanh methods. Also, the most general Lie point symmetry group of the KBK equation are presented using the basic Lie symmetry method. As well as, the non-classical and weak symmetries of this equation, as well as the corresponding similarity reductions, are investigated. Finally, the classical and non-classical symmetries of KBK and KdV-Burgers (KB) equations are compared.

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Travelling Wave Solutions for the KdV‐Burgers‐Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

Cited by 17 publications

References 34 publications

Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

Traveling wave solutions for a generalized Kawahara and Hunter-Saxton equations

Some exact solutions of KdV-Burgers-Kuramoto equation

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