Solution of the three-wave resonant equations with one wave heavily damped

Abstract

The three wave equations in the limit where the waves at the upper two frequencies are undamped and the lowest frequency mode is heavily damped so that its dynamic equation becomes γ3a3=K*a1a2,are considered.These equations are solved (by quadrature) in two dimensions and time subject to arbitrary initial and boundary conditions. Illustative examples arising in tokamak heating by lower hybrid waves are presented.