Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: Exact traveling wave solutions and analysis

Alquran, Marwan; Jaradat, Imad; Băleanu, Dumitru

doi:10.1016/j.cjph.2019.01.005

“…Another goal of this work is to present the Kudryashov-expansion method [24,25,26,27,28] to seek other physical-type solutions that the TMBH could have. By the wave transform η = x − ct, the TMBH is reduced to the following simplified differential equation…”

Section: Kudryashov-expansion Methodsmentioning

confidence: 99%

Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals

Alquran

¹

,

Sulaıman

²

,

Yusuf

³

2021

Self Cite

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New two-mode version of Burger-Huxley equation is derived using Korsunsky's operators. The new model arises in the applications of nerve fibers and liquid crystals and describes the interaction of two symmetric waves moving simultaneously in the same direction. Kink-soliton, singular-kink-soliton and singular-periodic solutions are obtained to this model by means of the simplified bilinear method, polynomial-function method and the Kudryashov-expansion method. A comprehensive graphical analysis is conducted to show the physical aspects of this new type of nonlinear equations. Finally, all obtained solution are verified by direct substitution in the model.

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“…Another goal of this work is to present the Kudryashov-expansion method [24,25,26,27,28] to seek other physical-type solutions that the TMBH could have. By the wave transform η = x − ct, the TMBH is reduced to the following simplified differential equation…”

Section: Kudryashov-expansion Methodsmentioning

confidence: 99%

Kink-Soliton, Singular-Kink-Soliton and Singular-Periodic Solutions for a New Two-Mode Version of the Burger-Huxley Model: Applications in Nerve Fibers and Liquid Crystals

Alquran

¹

,

Sulaıman

²

,

Yusuf³

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

New two-mode version of Burger-Huxley equation is derived using Korsunsky's operators. The new model arises in the applications of nerve fibers and liquid crystals and describes the interaction of two symmetric waves moving simultaneously in the same direction. Kink-soliton, singular-kink-soliton and singular-periodic solutions are obtained to this model by means of the simplified bilinear method, polynomial-function method and the Kudryashov-expansion method. A comprehensive graphical analysis is conducted to show the physical aspects of this new type of nonlinear equations. Finally, all obtained solution are verified by direct substitution in the model.

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“…The Kudryashov-expansion technique [32][33][34][35] proposes the solution of (1.4) as a polynomial of the variable Z, namely…”

Section: Kudryashov Solutions Of Tmfkdvmentioning

confidence: 99%

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

Ali

¹

,

Alquran

²

,

Jaradat

³

et al. 2019

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In this work, we present a new two-waves' version of the fifth-order Korteweg-de Vries model. This model describes the propagation of moving two-waves under the influence of dispersion, nonlinearity, and phase velocity factors. We seek possible stationary wave solutions to this new model by means of Kudryashov-expansion method and sine-cosine function method. Also, we provide a graphical analysis to show the effect of phase velocity on the motion of the obtained solutions. MSC: 35C08; 74J35

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Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: Exact traveling wave solutions and analysis

Cited by 70 publications

References 30 publications

Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals

Kink-soliton, singular-kink-soliton and singular-periodic solutions for a new two-mode version of the Burger–Huxley model: applications in nerve fibers and liquid crystals

Kink-Soliton, Singular-Kink-Soliton and Singular-Periodic Solutions for a New Two-Mode Version of the Burger-Huxley Model: Applications in Nerve Fibers and Liquid Crystals

Stationary wave solutions for new developed two-waves’ fifth-order Korteweg–de Vries equation

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