Discontinuity structures and solitary waves in electromagnetic hydrodynamics associated with linear and nonlinear Alfvén wave resonances

Nondissipative and weakly dissipative discontinuity structures are considered. A special numerical method for studying periodic waves is used. The location of branches of periodic solutions is investigated. Solitary waves and nondissipative discontinuity structures are sought as limiting solutions. It is found that, in addition to the resonance of long Alfvén waves with short fast and slow magnetosonic waves, there is also resonance with long waves, which leads to the occurrence of hybrid-type solitary waves and hybrid-type discontinuity structures. Partial differential equations are solved to find out if the found structures are actually observed.