Normal form analysis and chaotic scenario in a Schrödinger–Boussinesq system

The coupled Schrödinger–Boussinesq system is known to describe various physical processes in plasma. On the one hand it describes high-frequency upper-hybrid waves coupled to appropriate low-frequency ones such as magnetosonic modes and on the other hand it also describes the Langmuir oscillations in plasma. The system has been seen to be integrable for very specialised values of the parameters. Here in this communication we have analysed the same set near the resonant region M→1 (where M stands for the Mach number) in a different way. A parameter p=eg2/σ has been identified, whose variation exhibits the change in the nature of the fixed point and defines the critical region best suited for normal form analysis. This reduces the four-dimensional system to a two-dimensional one. The nature of this reduced system is analysed graphically. In a certain region of p the system showed chaoticity and it was studied through Lyapunov exponent, Poincaré section and phase space analysis.