Abstract
A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions to Nonlinear Evolution Equation (NLEE) containing parameters of particular importance in biophysics and nanobiosciences. For this equation, we find trigonometric, hyperbolic, rational, and exponential function solutions, as well as soliton-like pulse solutions. A comparison with other approach indicates the legitimacy of the approach we devised as well as the fact that our method offers extra solutions. Finally, we plot 2D, 3D and contour visualizations of the exact results that we observed using our approach using appropriate parameter values with the help of software Mathematica 10.
Highlights
Various fields of applied mathematics, engineering and mathematical physics, such as hydrodynamics, solid state physics, fiber optics, biology, fluid mechanics, plasma physics, geochemistry, and chemical systems confront multiple technical challenges in developing an understanding of nonlinear phenomena
Calculating numerical and analytical solutions of nonlinear evolution equations (NLEEs), notably solitary and travelling wave solutions, is crucial in soliton theory [1]. Symbolic software such as Maple, Mathematica, and Matlab have been popular for determining numerical solutions, exact solutions, and analytical solutions to Nonlinear Evolution Equation (NLEE)
Based on polyelectrolyte characteristics of cylindrical biopolymers, we develop a new model for ionic waves along MTs in this paper
Summary
Various fields of applied mathematics, engineering and mathematical physics, such as hydrodynamics, solid state physics, fiber optics, biology, fluid mechanics, plasma physics, geochemistry, and chemical systems confront multiple technical challenges in developing an understanding of nonlinear phenomena. Calculating numerical and analytical solutions of nonlinear evolution equations (NLEEs), notably solitary and travelling wave solutions, is crucial in soliton theory [1]. Using the modified extended tanh function approach, Sekulic et al [13] analyzed the equation of MTs as a nonlinear RLC transmission line to get solitary wave solutions. The improved generalized Riccati equation mapping method was used by Zayed et al [24] to solve a nonlinear partial differential equation representing the dynamics of ionic currents along microtubules and construct travelling wave solutions. The goal of this research is to use the modified exp-function approach to find new exact solutions to nonlinear PDEs of particular relevance in nanobiosciences, such as transmission line model of nanoionic currents along microtubules, which play a vital role in cell signaling. Comparison of the newly obtained solutions with the existing solutions in the literature is given in the form of the table which shows that our solutions are new and more general
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