Roger Dashen
Phys. Dept., Univ. of California, San Diego, La Jolla, CA 92037
Daniel Wurmser
Gregory Orris
Naval Res. Lab., Washington, DC 20375-5350
A new parabolic equation for range-dependent sound speeds has been developed by modifying a procedure borrowed from quantum mechanics. The forward and backward propagating solutions are decoupled order by order by repeated applications of the Foldy--Wouthuysen transformation. The result includes energy-conserving terms which are proportional to the second range derivative of the sound speed squared. Physically, the technique has identified the terms responsible for heretofore anomalous refractive effects which accumulate during propagation as a result of rapid oscillations between the forward and backward propagating solutions. Moreover, this phenomenon does not result in permanent energy transfer between the two types of solutions. [Work supported by ONR.]