Batch of solitary waves in a two-dimensional asymmetric Davydov-Scott model for coherent energy transport in the alpha-helix

This study presents a two-dimensional asymmetric generalized Davydov-Scott model to analyze the nonlinear dynamics of exciton-phonon interactions in protein alpha helices. The asymmetry parameter β (0 ≤ β ≤ 1) accounts for the structural and environmental heterogeneities of proteins, linking the symmetric Davydov (β=1) and antisymmetric Scott (β=0) models. From a Hamiltonian approach, we derive a two-dimensional cubic nonlinear Schrödinger equation (2 D-CNLSE) governing the transport of amide-I vibrational energy. Linear stability analysis via modulational instability (MI) shows that the growth rates obtained, influenced by the parameters J, χ, and β, correspond to timescales (picoseconds to nanoseconds) relevant to biological processes. By applying an extended direct algebraic method, we analytically construct bright, dark, double bright and multi hump solitons; confirm their stability numerically; and show that each type corresponds to a distinct biological function: energy storage, directional transfer, allosteric regulation, cooperative transfer, and collective modes. These results offer new insights into the mechanisms of energy transport and storage in biomolecules, with implications for understanding processes such as muscle contraction, cell signaling, and protein folding.