Explicit solution of certain nonlinear difference equations by using power polynomials

The paper presents new results related to explicit solutions of certain nonlinear difference equations which appear very often in studies of two linear simultaneous partial differential equations with damping terms. It is shown that the determination of the ratios of solutions corresponding to transversal and longitudinal signals can be based on particular forms of power polynomials in indeterminate y = y(s) depending on the equationsʹ coefficients and the complex frequency s. Some basic properties of the power polynomials are investigated, and links between them are established. Problems involving equalities and limits are also solved.