Modulational instability and travelling waves in (2+1)-dimensional alpha-helix protein chains with diagonal and off-diagonal couplings

This paper examines the dynamics of a single-stranded alpha-helical protein chains in two dimensions. It establishes that the dynamics of such a system is governed by a two-dimensional continuous cubic-quintic nonlinear Schrödinger equation. With the use of modulational instability, linear stability analysis is performed. It appears that the amplitude of the growth rate and the number of regions of instability are affected by certain coupling parameters of the system such as diagonal and off-diagonal coupling constants. The new (2+1)-extended direct algebraic method is applied to construct analytical solutions. Anti-kink, kink, dark and bright solitary waves are some results of propagating waves in the studied protein chains. Numerical simulations are performed to materialize these waves as stable.