THE GENERALIZATION OF THE VAN DER WAALS EQUATION WITHIN THE CUBIC FUNCTION

Abstract

A model has been developed that generalizes the Van der Waals formula at the intersection of the condensation line with the subcritical isotherm. Its parameters correspond to a periodic solution on a discriminant curve, where it is limited by a curve defined by a zero discriminant and a pair of multiple real roots. The model reproduces Nigmatulin–Taleyarkhan bubble thermonuclear fusion until the collapse of spherical bubbles in a two-phase medium, in which D-acetone nuclei condense at a resonance frequency of 20 kHz. In a two-phase medium, the bordering curve is essentially the surface of a bubble, inside which the D-acetone nuclei are concentrated on the discriminant curve. The model parameters were determined using Van der Waals corrections. As a result of the generalization, a new solution was obtained - a soliton in the form of a function arctan, on which a ball is strung, therefore it can be used to explain ball lightning and St. Elmo's fire.