Some problems of the uniqueness of the re-establishing the Brunt-Väisälä frequency using dispersion curves (Q2761264)

The author considers a mathematical model of stratified ocean with constant depth. The dispersion curves of internal gravity waves are determined using the boundary value problem \(u''+ q(x)u'+ \frac{q(x)-\eta^2}{\eta^2-F^2} \xi^2u = 0\), \(u'(0)= -\xi^2(\eta^2-F^2)^{-1}u(0)\), \(u(1)=0\). Here the parameters \(\xi\) and \(\eta\) represent the wave number and frequency of free harmonic oscillations, and \(F\) is related to the ocean depth and Coriolis parameter. Studied is the uniqueness of solution to the equation for the square of Brunt-Väisälä frequency. Some examples are given.