Quasistationary solutions to the resonant dispersion equation with allowance for viscosity

A smooth stationary-wave solution to the nonlinear resonant dispersion equation is constructed by combining the asymptotic methods of different scales and sewing the asymptotic expansions with allowance for viscous loss. In the limit of zero viscosity this solution becomes singular. In this case, the energy loss is shown to decrease (rather than grow) in proportion to viscosity as for any wave with a smooth profile. This type of solution is referred to as quasistationary.