Abstract: 

We discuss recent results on equilibria and stability in plasma models. We discuss the construction of magnetic confinement equilibria for the Vlasov–Maxwell system, including z-pinch, \theta-pinch, and screw-pinch configurations, and present a Hamiltonian framework for their stability analysis. We also consider the Euler–Poisson system, highlighting its solitary-wave dynamics and connection to the KdV equation in the near-sonic regime.