[2] The problem of description of distortions of radio wave pulses in the media with dispersion was posed about a century ago [Brillouin, 1914; Sommerfeld, 1914] and still remains vital because of its practical significance. A special place in this field of research is occupied by the problems of propagation of radio wave pulses through the ionosphere. The works on this subject involve analysis of the data obtained by performing, analytically or numerically, inverse Fourier transformation of the current frequency spectrum of a propagating signal. In some investigations magnetic field is ignored [Denisov, 1951; Gershman, 1952; Ginzburg, 1967; Kozaki and Mushiake, 1969; Tyorina, 1967, 1972; Wait, 1965; Wait and Spies, 1966; Zhekulin, 1938], and in some studies it is taken into account [Bahar and Agraval, 1979; Brookner, 1978; Chang and Helliwell, 1980; Chen and Yen, 1972, 1973; Kalluri, 1989; Kozaki and Mushiake, 1970; Kretov et al., 1991; Zhang and Tschu, 1987] (see also the review of McIntosh and Malaga [1980]). The majority of the authors use a narrowband signal approximation which allows one to considerably simplify analysis of distortions of, as a rule, Gaussian or rectangular pulses, but with appreciable restrictions on parameters of the problem. The usual practice is also to use a collisionless plasma approximation. In the case of wideband pulses used in communication, radar, and sensing of the environment, such restrictions are inapplicable, and the inverse Fourier transformation can be performed only numerically [see, e.g., Vishin et al., 2003, 2004]. In this paper we present solution of the problem on propagation of a radio wave pulse in isotropic and gyrotropic collisional cold plasmas which is not based on the frequency representation and allows for analytical description of spatial-temporal evolution of a pulse with the initial envelope of a sufficiently general form, including pulses with a linear frequency modulation.
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