Nondissipative discontinuity structures and solitary waves in solutions to equations of two-fluid plasma in the electromagnetic hydrodynamics approximation

Numerical methods for the equations of electromagnetic hydrodynamics are described, periodic waves, solitary waves, and nondissipative discontinuity structures are studied. It is found that the wave amplitude cannot exceed certain values, which leads to wave overturning. Nondissipative discontinuity structures are constructed as limits of sequences of solitary waves. Estimates of the maximum amplitudes at which solitary waves exist can be used to estimate the maximum amplitudes of discontinuities. The location of branches of periodic solutions is investigated. It is shown that the discontinuity of the long-wave branch of fast magnetosonic waves does not correlate with the existence of transition to the short wave, which explains the occurrence of chaotic solutions. The study of slow magnetosonic waves showed that, at small and moderate amplitudes, there exists a solution that is close to a solitary wave.