The dynamics of coupled nonlinear waves is addressed in the framework of the angular model of microtubules. The semi-discrete approximation is used to write the dynamics of the lower and upper cutoff modes in the form of coupled nonlinear Schrödinger equations. The linear stability analysis of modulational instability is used to confirm the existence of soliton solutions, and the growth-rate of instability is shown to be importantly influenced by the dipolar energy. Single mode solutions are found as breathers and resonant kink, while the coupled mode introduces a kink envelope solution, whose characteristics are discussed with respect to the dipolar energy. The found solution is shown to be robust, which is important for energy transport in the Polymerization/depolymerization mechanism of protofilaments.
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