Bifurcation and stability analysis of solitary waves in dissipative systems governed by extended nonlinear Schrödinger equation with deformable substrate potential

In this article, we discuss bifurcation theory in the context of solitons gap dynamics governed by an extended nonlinear Schrodinger equation incorporating complex nonlinear interactions (cubic and quintic) within the framework of an asymmetric double-periodic Remoissenet–Peyrard type potential. The deformability of this potential serves as an active control parameter that enables precise adjustment of its energy landscape to model and steer the properties of reconfigurable smart materials. Using the bifurcation method, we solve the extended nonlinear Schrodinger equation and analyse the stability of equilibrium points. We observe that the deformability parameter enables the controlled emergence of additional metastable states, a fundamental property for designing multi-memory materials. Furthermore, we study modulational instability and again observe the impact of this same deformability parameter on the system’s stability. It emerges that a slight deviation of this parameter from zero induces an abrupt phase transition, representing a fine control threshold highly desirable for designing ultra-sensitive nonlinear switches or sensors where a small external stimulus triggers a massive functional response. All these theoretical predictions, establishing the foundations for active control, have been rigorously validated through direct numerical simulations, confirming the potential of our approach to guide the design of next-generation smart materials with dynamically reconfigurable properties.