Based on the perturbation theory, an investigation on reflection and refraction of nonlinear wave on a boundary in fluids or solids was carried out a familiar result was obtained that the second harmonic wave always satisfies an inhomogeneous wave equation. In order to find its special solution, the method of separated variables as well as Lagrange's method of variation parameters were invoked , and a trouble to the boundary-value problem of nonlinear acoustics will consequently result in that a separation constant is to be determined. In this paper , the constant was determined and the special solution was given uniquely. It is shown that a paradox will occur unless we select a special solution from the following two solutions, which are accumulation along the direction either parallel to or perpendicular to the boundary plane. Whether one can be selected depends on the boundary situation. By using the theory, the reflection and the refraction on a plane boundary were analysed. Furthermore, it is pointed out that this theory can deal with all of the boundary-value problems in nonlinear acoustics.
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