Periodic and Solitary Waves and Nondissipative Discontinuity Structures in Electromagnetic Hydrodynamics in the Case of Wave Resonance

A numerical method is described for studying periodic waves, solitary waves, and nondissipative discontinuity structures for the equations of electromagnetic hydrodynamics. The arrangement of branches of periodic solutions is analyzed. Solitary waves are obtained as limiting solutions of sequences of periodic waves, and nondissipative discontinuity structures are obtained as the limits of sequences of solitary waves. It is shown that a discontinuity of the long-wave branch of fast magnetosonic waves does not correlate with the existence of a transition to the short-wave branch, which leads to the emergence of chaotic solutions in the absence of dissipation. The study of slow magnetosonic waves has shown that for small and moderate amplitudes there exists a solution close to a solitary wave. Approximate solitary waves of hybrid type are revealed that represent combinations of an Alfvén and a slow magnetosonic wave.