Korteweg de Vries Surface Solitons at Plasma Interfaces

We analyse the propagation of nonlinear waves along a slab of magnetized non-homogeneous bounded plasma under gravity. We prove that small Mach number and weakly dispersive Korteweg de Vries solitons propagate along the magnetic field. These solitons produce negligible vorticity, electrical current and density fluctuations. Conditions are worked out for them to be of the sausage or kink mode, of the dark or bright type and for their speed to be super- and sub-Alfv\'{e}nic. An example of the sausage, bright, super-Alfv\'{e}nic soliton is also reproduced by ab-initio two-dimensional numerical simulations of the fully compressible MHD equations.