Low-frequency nonlinear stationary waves and fast shocks: Hydrodynamical description

Stationary one-dimensional nonlinear waves in two-fluid hydrodynamics are studied analytically in the assumption of polytropic pressure and massless electrons. Particular attention is paid to the presence of soliton solutions, which exist when the asymptotic plasma velocity is in the range v+2<v2<vF2 or vSL2<v2<v−2, where vSL, vI, vF, and vS are the slow, intermediate, fast and sound speeds, respectively, and v−=min(vS,vI), v+=max(vS,vI). A general nonlinear solution is derived in the parametric representation. Inclusion of weak dissipation changes qualitatively the behavior of solutions allowing for fast shock-like solutions. A generalized expression for the whistler precursor wavelength is derived.