A procedure for studying wave propagation in ionospheric plasma based on the use of a bicharacteristic system and an extended bicharacteristic system of equations that allows the caustic structure to be determined has been developed. Propagation of an ordinary and extraordinary waves in an anisotropic plasma, in a one-layer and two-layer models, in the presence of local irregularities, has been numerically simulated. With the use of the radiotomography data, the effect of the equatorial anomaly on the propagation of decameter waves has been investigated.

We present the results of the radiotomographic imaging of the artificial ionospheric disturbances obtained in the recent experiments on the modification of the midlatitude ionosphere by powerful HF radiowaves carried out at the Sura heater. Radio transmissions from low orbital PARUS beacon satellites recorded at the specially installed network of three receiving sites were used for the remote sensing of the heated ionosphere. We discuss the possibility to generate acoustic‐gravity waves (AGWs) with special regimes of ionospheric heating (with the square wave modulation of the effective radiated power at the frequency lower than or of the order of the Brunt‐Vaisala frequency of the neutral atmosphere at ionospheric heights during several hours) and present radiotomographic images of the spatial structure of the disturbed volume of the ionosphere corresponding to the directivity pattern of the heater, as well as the spatial structure of the wave‐like disturbances, which are possibly heating‐induced AGWs, diverging from the heated area of the ionosphere. We also studied the HF propagation of the pumping wave through the reconstructed disturbed ionosphere above the Sura heater, showing the presence of heater‐created, field‐aligned irregularities that effectively serve as “artificial radio windows.”

Theoretical and applied results obtained in the theory of diffraction and propagation of electromagnetic waves with the use of methods of wave catastrophes are reviewed. The basic concepts of the theory are considered: classification of wave catastrophes, methods for constructing uniform asymptotics applied to describe fields in such regions, and analysis of the field structure. A general description of classes of special functions involved in uniform asymptotic decompositions of wave fields, properties of these functions, and methods of their calculation are presented. Applied problems that are solved efficiently by means of methods of wave catastrophes are discussed.

A numerical simulation of single-hop and double-hop propagation of frequency-modulated signals in anisotropic ionospheric plasma is performed on the basis of a numerical solution to a space–time Hamil

Methods of mathematical simulation of propagation of short radio waves in the Earth’s ionosphere are considered. Simulation is performed with allowance for new models of the Earth’s magnetic field, the electron concentration in the ionosphere, and experimental data obtained by means of the radio tomography method. Results of application of extended bicharacteristic system methods, the Maslov canonic operator method, and the catastrophe theory as the mathematical apparatus developed for the considered problems are described.

Propagation of frequency-modulated signals in an anisotropic medium (Earth’s ionosphere) is numerically simulated with allowance for the effect of the electron collision frequency on...