A time-dependent propagation of nonlinear magnetosonic waves in the interplanetary space with solar wind

A magnetosonic wave is a longitudinal wave propagating perpendicularly to the magnetic fields and involves compression and rarefaction of the plasma. Lee and Kim (2000) investigated the theoretical solution for the evolution of nonlinear magnetosonic waves in the homogeneous space which adopt the approach of simple waves. We confirm the solution using a one-dimensional MHD code with Total Variation Diminishing (TVD) scheme. Then we apply the solution for the solar wind profiles. We examined the properties of nonlinear waves for the various initial perturbations at near the Lagrangian (L1) point. Also we describe waves steepening process while the shock is being formed by assuming different timescales for a driving source.