Investigation of solitons structures for nonlinear ionic currents microtubule and Mikhaillov-Novikov-Wang dynamical equations

In this work, we analysis the novel behavior of solitons to the nonlinear evolution equations describing the ionic currents microtubule and Mikhaillov-Novikov-Wang dynamical equations under an auxiliary equation approach. As a result, a variety of solitons solutions are achieved such as singular bright solitons, kink solitons, singular dark solitons and anti-kink solitons. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering including nonlinear optics, material energy, soliton wave theory, computational fluid mechanics, system identification, earthquake modeling, water wave mechanics, signal transmission, and optical fibers. We designed the utilized approach to be reliable and accurate, with precise for analytical results.