The Cauchy problem for the equation of internal waves

The Cauchy problem for the equation of internal waves in a continuously stratified fluid is considered. The uniqueness theorem is demonstrated, and a formula is derived for the explicit representation of the solution through integrals whose kernels contain Sekerzh-Zen'kovich's (1979) fundamental solution of the internal-wave operator and its derivative with respect to time. An asymptotic analysis of the solution in the 'far zone' and for large values of dimensionless time is presented.