Determination of background parameters of weakly dispersing stratified shallow water

A method for determining the background parameters of weakly dispersing media is formulated within the framework of the theory of low-intensity wave bores in such media. An analytical model of an undular (cnoidal) bore on a pycnocline of a stratified shallow sea is used to obtain expressions for calculating the coefficients of the extended Korteweg–de Vries equation: the velocities of linear internal waves, high-frequency dispersion, quadratic and cubic nonlinearities, i.e., the parameters characterizing the hydrophysical background over which the bore propagates. These parameters are calculated from data of direct measurements of bore characteristics: their waveforms, nonlinear velocity, mass and amplitude of leading solitons, as well as the frequencies of the waves that close the region in which the bore propagates. The efficiency of the proposed method is confirmed by the results of numerical simulation.