Solitonic excitations and interactions in an α-helical protein modeled by three coupled nonlinear Schrödinger equations with variable coefficients

Governing the molecular excitations associated with bioenergy transport in an α-helical protein through the soliton modes, three-coupled higher-order nonlinear Schrödinger equations with variable coefficients are investigated via symbolic computation. Using Bell polynomials, a bilinear form and Bäcklund transformation are derived for this model. Furthermore, explicit N-soliton solutions are constructed in terms of the double Wronskian determinant. Solitonic excitations are found to remain stable against the disorders of the parameters under certain constraints. Finally, propagation characteristics and interactions of the solitonic excitations are discussed. Soliton amplitudes are related to the energy modulation coefficients, and both the soliton properties and energy distribution during the interactions are affected by the inhomogeneity coefficients of the protein with time-dependent disorders.