Most of the time, wave propagation in musical wind instruments is justifiably considered to be linear. The acoustic propagation inside the bore of the instruments may then be described though a linear formalism both in the time and in the frequency domains : impedance, admittance, transmission line theory, convolution …

A well-known counter-example is the case of brass instruments (especially trumpets, trombones like instruments) at high sound level. In this case, the nonlinear effects become dominant. They account for the graduated waveshape distortion due to their cumulative nature which eventually leads to the arrival of shock-waves.

We present an exact method to solve a one-dimensional nonlinear wave equation in a dissipative non homogeneous media when the damping is frequency-independent. This work was motivated by the case of brass musical instruments. Though in that latter case, the medium is homogeneous, our approach is more general. Sound examples will be presented to emphasize the influence of nonlinear propagation effects in sound synthesis.