Makarenko N.I., Perevalova E.G.
A theoretical model of internal solitary waves with large amplitude in a weakly stratified fluid is considered. It is assumed that the background density profile of liquid linearly or exponentially depends on the depth. It was shown that the inverse problem of restoring the coefficient of the density fine structure based on the known amplitude dispersion curve is reduced to the solution of a linear Fredholm integral equation of first kind with the special form of the kernel. In the case of the polynomial stratification a one-to-one correspondence is established between the density coefficient and the dispersion function.