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, Marwan; Sulaıman, Tukur Abdulkadir; Yusuf, Abdullahi

doi:10.1007/s11082-021-02883-2

Cited by 31 publications

(5 citation statements)

References 45 publications

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“…The current involved approach has been reported in the literature and according to this, there are many families of solutions satisfying eq. ( 23) [61][62][63]. Before remembering the solutions families cases according to the literature, let us also remind that, N is assessed by fulfilling the balance principle between the highest order of the linear derivative term and the highest order of the nonlinear term inside eq.…”

Section: Mathematical Description Of the Polynomial Expansion Methodsmentioning

confidence: 99%

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Fendzi-Donfack,

Fotoula,

Jantschi

et al. 2024

Preprint

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This work aims to delve exact physical wave solutions of nonlinear diﬀerential-diﬀerence equations with beta-derivative leading the conduction of nerve impulse dynamics in coupled nerve ﬁbers. The technique performed here names the polynomial expansion method. By employing a new variable through a fractional complex transformation, we turn the electrical model equation to a second-order elliptic nonlinear ordinary diﬀerential equation with two free parameters including the semi-discrete approximation. We extract short pulse, kink, anti-kink, singular kink/anti-kink and kink-rogue solitary waves as solutions of the derived elliptic nonlinear ordinary diﬀerential equations. By carrying out these various solutions, we peruse the dynamical behavior of the current nerve ﬁbers model by investigating their linear stability. We also study the dynamics of the model by applying the ﬁxed points theory and derive the related Jacobian matrix. Throughout the convenient physiological parameters values and signs, we display some 3D modulational instability zones. Furthermore, we also exhibit 3D and 2D graphs presenting the shapes of new pursued solitary waves. The numerous solutions families obtained and plotted help us to show the fractional-order parameter eﬀects in addition of the nerve ﬁber diameter on the amplitude and speed of the nerve impulse propagating inside the coupled nerve ﬁbers. The good or bad coordination of the movement inside the human parts can be explain through the amplitude varying, speed modiﬁcation of the nerve impulse ﬂowing into the coupled nerve ﬁbers. Aiming to this, we make the evolved mathematical framework accessible and highlight potential medical and biological applications. In addition, we enhance the understanding of nerve conduction mechanisms in myelinated ﬁbers.

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Section: Mathematical Description Of the Polynomial Expansion Methodsmentioning

confidence: 99%

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Fendzi-Donfack,

Fotoula,

Jantschi

et al. 2024

Preprint

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“…Three numerical schemes will be used to solve (2.3); the Kudryashov-expansion method [6][7][8], a new modification of the sine-cosine function method [9][10][11], and the polynomial function method [12][13][14].…”

Section: Pochhammer-chree Equation With P =mentioning

confidence: 99%

Convex-rogue, half-kink, cusp-soliton and other bidirectional wave-solutions to the generalized Pochhammer-Chree equation

et al. 2022

Self Cite

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The generalized Pochhammer-Chree equation is considered and studied for different orders of its nonlinearity terms. The Kudryashov-expansion method is used and bidirectional kink, singular-kink, rogue-periodic, and V-shaped wave-solutions are obtained. Moreover, we modify the sine-cosine function method to accommodate the current model and obtain symmetric half-kink, convex-rogue, and cusp bidirectional waves. On the other side, a graphical analysis is conducted to identify the physical shapes of the obtained solutions to the proposed model. Finally, the polynomial function method is implemented to validate the reported solutions.

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“…10 Considering this organic compound and its application in LC display screens, numerous studies have already been carried out. [11][12][13][14][15][16] Here, the study of nonlinear optical and electro-optic properties of the PAA liquid crystal is carried out. The PAA liquid crystal possesses high values of hyperpolarizability and anisotropic polarizability which support its use in nonlinear applications.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanical studies of p-azoxyanisole and identification of its electro-optic activity

Kumar

Mishra

Kumar

et al. 2023

Phys. Chem. Chem. Phys.

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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

Cited by 31 publications

References 45 publications

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Enhanced analysis of soliton-like pulses in space-time fractional beta-derivatives coupled nerve fibers with application insights

Convex-rogue, half-kink, cusp-soliton and other bidirectional wave-solutions to the generalized Pochhammer-Chree equation

Quantum mechanical studies of p-azoxyanisole and identification of its electro-optic activity

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