Quasi-stationary evolution of cubic-quintic NLSE drop-like solitons in DNA-protein systems

Nonlinear molecular excitations in DNA have traditionally been modelled using the nonlinear Schr\"odinger equation (NLSE). An alternative approach is based on the plane-base rotator model and the SU(2)/U(1) generalized spin coherent states, which leads to a cubic quintic NLSE. Higher-order nonlinearities are particularly useful for modelling complex interactions, such as those in DNA-protein systems, where multiple competing forces play a significant role. Additionally, the surrounding viscous medium introduces dissipative forces that affect the propagation of molecular excitations, leading to energy dissipation and damping effects. These damping effects are modelled using the quasi-stationary method, which describes the system's near-equilibrium behaviour. In this work, we explore the evolution of nonlinear molecular excitations in DNA-protein systems, accounting for damping effects, and discuss potential applications to the transcription process.