Before revision:  We use the problems of two ideal fluid waveguides as examples, i.e., one with a constant sound speed in shallow water and one with a Munk sound speed profile in the deep ocean.
After revision:  This method is currently suitable only for range-independent waveguides. Taking three ideal fluid waveguides as examples, i.e., one with a constant sound speed in shallow water and one with a Munk sound speed profile in the deep ocean.