Abstract
Nonlinear hydromagnetic waves in a hot collisionless plasma are investigated, on the basis of a two-fluid model of plasma composed of cold ions and isothermal electrons. In this paper (Part I), wave trains propagating across a magnetic field are studied analytically. An existence condition for solutions is exactly obtained, and the typical wave profiles are given graphically. These waves are qualitatively similar to those in a cold plasma. The width of the wave is of the order of the geometric mean between the Larmor radii of the electron and of the ion. As limiting cases, they include two special solutions which have already known, that is, (i) solitary wave solutions in a hot plasma, (ii) wave train solutions in a cold plasma.
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