A new family of asymptotic solutions of the Helmholtz equation can be derived. It is shown that new solutions are regular at caustics and turning points and do not require any special functions.

The numerical problems of SWAM'99 workshop are quite challenging for any method of sound field calculation. This report presents a detailed description of the enhanced ray theory approach briefly outlined in Ref. 2. It contains a new method of phase and amplitude computation along the ray, a new method of calculation of eigenrays, and a new method of analytic approximation of sound-speed and density. An application of these methods is presented.

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The Fresnel formulas for reflection and refraction coefficients at the boundary between two liquid medias assume discontinuity of media properties at the boundary. In many physical applications this assumption is too strong. A recent report considers a model problem with the following properties: n2(z)=3D[n21<th>exp(αz)+n20<th>exp(−αz)/e xp(αz)+exp(−αz)]ρ(z)=3D[ρ1<th>exp(αz)+ρ0<th >exp(−αz)/exp(αz)+exp(−αz)] which are representing a smoothed boundary. An exact solution of Euler equations is derived in a form of plane waves and fast converging series. Physical effects are investigated for reflection and refraction of plane and spherical harmonic and pulse waves in such a model.