<b><i>N</i></b>soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3 1) dimensions

Su, Yu; Toda, Kouichi; Sasa, Narimasa; Fukuyama, Takeshi

doi:10.1088/0305-4470/31/14/018

Cited by 123 publications

(50 citation statements)

References 18 publications

(27 reference statements)

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“…It was Yu et al [34] who extended the (2+1)-dimensional BogoyavlenskiiSchiff equation [35], (11) to the (3+1)-dimensional nonlinear evolution equation in the form of (9).…”

Section: Application To the (3+1)-dimensional Potential Ytsf Equationmentioning

confidence: 99%

The Modified (G'/G)-Expansion Method for Nonlinear Evolution Equations

Zhang

Sun

et al. 2011

Zeitschrift Für Naturforschung A

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A modified (G /G)-expansion method is proposed to construct exact solutions of nonlinear evolution equations. To illustrate the validity and advantages of the method, the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation is considered and more general travelling wave solutions are obtained. Some of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions, and rational solutions contain an explicit linear function of the variables in the considered equation. It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

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“…It was Yu et al [34] who extended the (2+1)-dimensional BogoyavlenskiiSchiff equation [35], (11) to the (3+1)-dimensional nonlinear evolution equation in the form of (9).…”

Section: Application To the (3+1)-dimensional Potential Ytsf Equationmentioning

confidence: 99%

The Modified (G'/G)-Expansion Method for Nonlinear Evolution Equations

Zhang

Sun

et al. 2011

Zeitschrift Für Naturforschung A

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“…introduced by Zhang et al [30] and Hu et al [31], while making the (3+1)-dimensional generalization from (2+1)-dimensional Calogero-Bogoyavlenkii-Schiff equation [32]:…”

Section: The (3+1)-dimensional Yu-toda-sasa-fukuyama Equationmentioning

confidence: 99%

Soliton Soltuions of Nonlinear Evolutions Equation by using the Extended Exp (-φ(ξ)) Expansion Method

Khater¹,

Zahran²

2016

IJCA

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In this research, we employ the extended exp(−ϕ(ξ))expansion method for the first time to obtain the exact and solitary wave solutions of the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation. We obtain the wide range of exact and solitary wave solutions of distinct physical structure. KeywordsExtended exp(−ϕ(ξ))-expansion method, The (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama equation, Traveling wave solutions, Solitary wave solutions.

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“…Consider two operators L and T which are called the non-isospectral Lax pair and given by Lψ = λψ, T ψ = 0, and λ being a non-isospectral parameter [23,25,26] independent of only x. Then the commutation relation:…”

Section: Lax Pair Of (23)mentioning

confidence: 99%