A Bilinear Bäcklund Transformation and N-Soliton-Like Solution of Three Coupled Higher-Order Nonlinear Schrödinger Equations with Symbolic Computation

A bilinear Backlund transformation is presented for the three coupled higher-order nonlinear Schrodinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Backlund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems.

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