Abstract
This work investigates a coupled generalized Schrödinger-Boussinesq system with a $ p $-power nonlinearity. These equations appear in several physical applications. To begin, we present a complete classification of infinitesimal point symmetries for the system. Then, low-order local conservation laws are derived using the multiplier method, providing conserved quantities such as momentum, mass, and charge. By introducing a potential variable, we derive a Lagrangian formulation for the potential system and find nonlocal conservation laws via Noether's theorem. Finally, we explore travelling wave solutions by reducing the governing equations to a coupled autonomous system of ordinary differential equations. Several families of solutions are constructed, and their physical relevance is discussed.