Average conservative chaos in quantum dusty plasmas

We consider a hydrodynamic model of quantum dusty plasma. prove mathematically that the resulting dust ion-acoustic plasma waves present property being conservative on average. Furthermore, we test this numerically, confirming its validity. Using standard techniques from study dynamical systems, as, for example, Lyapunov characteristic exponents, investigate chaotic dynamics and show numerically existence wide range parameter values. Finally, illustrate how organizes in space fixed values initial conditions, as Mach number diffraction are continuously varied.