Nonlinear model for magnetosonic shocklets in plasmas
  Exact nonlinear equations for magnetosonic shocklets in a uniform hot magnetoplasma are derived by using the nonlinear magnetohydrodynamic equations. Analytic as well as numerical solutions of the nonlinear equations are presented. Shock-like structures of the ion fluid velocity and magnetic field (or the plasma density) perturbations are obtained. The results may have relevance to the understanding of fast magnetosonic shocklets that have been recently observed by onboard instruments of the Cluster spacecraft at the Earth's bow shock. 
P.K. Shukla, B. Eliasson, M. Marklund, and R. Bingham