A possible method for finding the value of indeterminate near wave field of an expanding cylinder

A strict analytical solution of the wave equation with cylindrical symmetry in a region with mobile boundaries was obtained by the method of inverse problems with an allowance for the interaction of nonlinear arguments. The method is universal and applicable to solving both inverse and direct problems for arbitrary values of the initial radius and displacements. The solution describes a near wave field of an expanding plasma piston, including that formed in the initial moments of a pulsed process.