Transverse diffraction of weakly nonlinear waves for a first order quasi-linear system involving source-like terms

Making use of the ray theory and the method of asymptotic expansion of multiple scales, a study of the diffraction of weakly nonlinear waves in a direction transverse to the rays, through media described by dissipative or dispersive hyperbolic systems, is proposed. It is shown that the wave amplitude satisfies a generalized Zabolotskaya-Khokhlov equation in the dissipative case, or a generalized Kadomtsev-Petviashvili equation in the dispersive case. Moreover, plane, cylindrical and spherical waves are also investigated. The present approach is used to study wave diffraction in a heat-conducting fluid.