On traveling wave solutions for the transmission line model of nano-ionic currents along MTs arising in nanobiosciences

This paper presents many new soliton solutions in equation of nano-ionic currents along microtubules using an improved tan ( ϕ / 2 ) -expansion method, the generalized ( G ′ / G )-expansion technique and the Exp-function method. The abundant solutions including kink soliton solution, hyperbolic solution, trigonometric solution and bell-shaped soliton solutions are attained. Comparing our new results with the well-known results show that obtained solutions are the plenty types of three forms containing soliton, periodic and kink-singular solutions. The outcomes illustrate that the previously mentioned strategies are more effective than the Ansatz strategies as modified extended tanh-function applied by Sekulic̀ et al. (Appl Math Comput 218:3499–3506, 2011) and solitary wave ansatz method applied by Younis and Ali (Appl Math Comput 246:460–463, 2014). The mentioned methods are very simple and concise and can be also applied to other nonlinear partial differential equations. More importantly, the solutions found in this work can have significant applications in microtubules systems where solitons are used to nano-ionic structures.