Traveling wave solutions along microtubules and in the Zhiber–Shabat equation

Tala-Tebue, E.; Djoufack, Z.I.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kapche-Tagne, F.; Kofané, Timoléon C.

doi:10.1016/j.cjph.2017.03.004

Cited by 25 publications

(5 citation statements)

References 13 publications

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“…All the obtained analytical solutions have satisfied the model. When we compare our obtained results with the results in the literature [18,19] we observed that our result are newly constructed with the different solution structure. Therefore, with our available results, we can say that the Bernoulli sub-equation function method is simple and efficient mathematical tool that can be employed to various mathematical models.…”

Section: Discussionsupporting

confidence: 58%

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Novel Behaviors to the Nonlinear Evolution Equation Describing the Dynamics of Ionic Currents along Microtubules

et al. 2017

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Abstract. In this work, we consider the Bernoulli sub-equation function method for obtaining novel behaviors to the nonlinear evolution equation describing the dynamics of ionic currents along Microtubules. We obtain new results by using this technique. We plot two-and three-dimensional surfaces of the results by using Wolfram Mathematica 9. At the end of this manuscript, we submit a conclusion in the comprehensive manner.

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Section: Discussionsupporting

confidence: 58%

“…However, in this article, we explore the search for the new solutions to the transmission line models of nano-ionic currents along microtubules [18,19] by using the Bernoulli sub-equation function method (BSEFM) [20].…”

Section: Introductionmentioning

confidence: 99%

Novel Behaviors to the Nonlinear Evolution Equation Describing the Dynamics of Ionic Currents along Microtubules

et al. 2017

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“…where (8) is the equation describing the dynamics of the out-of-phase motion of a weakly inhomogeneous DNA model. It can be solved directly using the series expansion unknown function method [27] or the exponential rational function method [28]. In this paper, we are looking for the envelope soliton in the small amplitude approximation as a perturbed plane wave solution.…”

Section: Model Hamiltonian Of Dna Dynamics and Equations Of Motionmentioning

confidence: 99%

Nonlinear dynamics of DNA systems with inhomogeneity effects

Okaly

Mvogo

Woulaché

et al. 2018

Chinese Journal of Physics

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We investigate the nonlinear dynamics of the Peyrard-Bishop DNA model taking into account site dependent inhomogeneities. By means of the multiple-scale expansion in the semi-discrete approximation, the dynamics is governed by the perturbed nonlinear Schrödinger equation. We carry out a multiple-scale soliton perturbation analysis to find the effects of the variety of nonlinear inhomogeneities on the breatherlike soliton solution. During the crossing of the inhomogeneities, the coherent structure of the soliton is found stable. The global shape of the inhomogeneous molecule is merged with the shape of the homogeneous molecule. However, the velocity, the wavenumber and the angular frequency undergo a time-dependent correction that is proportional to initial width of the soliton and depends on the nature of the inhomogeneities.

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“…Equation 2plays an imperative role in many scientific applications arising in nonlinear optics, plasma physics and quantum field theory [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Several researchers obtained the different types of exact solutions of the Tzitzeica-Dodd-Bullough equation by applying numerous analytic methods such as, the tanh method [28], [29], the modified simple equation method [30], the bifurcation method [31], the modified tanh-coth function method [32], the ( ) '/ GG -expansion method [33,34], the improved -expansion method [35], the -expansion method [36], the modified Kudryashov method [37], an ansatz approach with the Jacobi elliptic function method [38], the exponential rational function method [39], [40], the exp and double exp function method [41], [42], the direct algebraic method [43], the novel exponential rational function method [44], the sine-Gordon expansion method [45] and the modified version of the improved -expansion method [46]. Interested reader can read the other references article herein [47], [48].…”

Section: Introductionmentioning

confidence: 99%

New closed-form soliton solutions for the tzitzeica dodd bullough equation arising nonlinear optics via three distinct re-liable approaches

Hawlader

Akter

2021

IJPR

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Tzitzeica Dodd Bullough (TDB) equation appears in the field of quantum field theory and nonlinear optics. In this article, we extracted abundant new soliton solutions with free choice of arbitrary parameters to the Tzitzeica-Dodd-Bullough (TDB) equation through the three separate methods such as the enhanced -expansion method, the improved -expansion method and the -expansion method by means of the wave transformation and the Painleve property. In these schemes, we formally derived some new closed form soliton solutions of the TDB equation through with symbolic computation package Maple. Soliton solutions are expressed by hyperbolic function, trigonometric function and rational function. The attained solutions are verified by symbolic computation software Maple 17. The attained solutions can be demonstrated by two-dimensional (2D) and three-dimensional (3D) graphs. Finally, it can be concluded that the adopted methods are very effective and well-suited to find new closed-form soliton solutions to the other nonlinear evaluation equations (NLEEs) with integer or fractional order.

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Traveling wave solutions along microtubules and in the Zhiber–Shabat equation

Cited by 25 publications

References 13 publications

Novel Behaviors to the Nonlinear Evolution Equation Describing the Dynamics of Ionic Currents along Microtubules

Novel Behaviors to the Nonlinear Evolution Equation Describing the Dynamics of Ionic Currents along Microtubules

Nonlinear dynamics of DNA systems with inhomogeneity effects

New closed-form soliton solutions for the tzitzeica dodd bullough equation arising nonlinear optics via three distinct re-liable approaches

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