M-shape and W-shape bright incite by the fluctuations of the polarization in a-helix protein

In this work, under consideration is the coupled system of nonlinear Schrödinger (NSL) and Boussinesq equations that serves as model to study the polarization fluctuation in α-helical protein. M-shaped and W-shaped solutions have been derived through the new modified Sardar sub-equation technique (SSEM). These solitons solutions define the polarization dynamics in the α-helical protein. The integration naturally leads to a constraint condition placed on the solitary wave variables which must hold for the solitary waves to exist. In addition, the standard linear stability analysis has permitted to study the behavior of the Modulation Instability (MI) gain spectra. Numerical simulation and physical interpretations of the acquired results are demonstrated. The derived structure of the acquired solutions give a rich platform to better understand the nonlinear dynamics in the α-helical protein.

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