Refined Model of Dynamics of Weakly Non-Spherical Bubbles with the Centers in a Straight Line

A mathematical model of interaction of weakly non-spherical gas bubbles in a liquid with the centers in a straight line is developed. This model is a system of ordinary differential equations of the second order in the radii of the bubbles, the spatial coordinates of their centers, and the amplitudes of their deviations from the spherical ones. It is of the sixth order of accuracy in terms of the ratio of the characteristic radius of the bubbles to the characteristic distance between them, which exceeds the accuracy of currently existing analogs.