Determining the control functions of wave processes in regions with mobile boundaries for a plasma cylinder of finite length expanding in a compressible medium

Exact analytical solutions of the wave equation in regions with mobile boundaries for the general case of cylindrical symmetry are obtained using an original method developed previously for solving inverse problems with allowance for the interaction of nonlinear arguments. The obtained solutions are universal and are valid for both inverse and direct problems. A method of eliminating logarithmic singularities, known to exist in the case of cylindrical symmetry, is proposed for the quantitative determination of the control functions of wave processes in regions with mobile boundaries, including the case of a plasma cylinder of finite length expanding in a compressible medium.