In the present paper, we study the nonlinear dynamics of microtubules relying on the known u-model. As a mathematical procedure, we use the simplest equation method. We recover some solutions obtained earlier using less general methods. These are kink solitons. In addition, we show that the solution of the crucial differential equation, describing nonlinear dynamics of microtubules, can be a bell-type soliton. The discovery of this new solution is supported by numerical analysis.

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