On the theory of acoustic solitons in a liquid with distributed gas bubbles

A close relation is established between numerical solutions to two systems of equations, viz., the two-level nonlinear wave dynamic model of a liquid with gas bubbles and the Korteweg-de Vries (KdV) equation. This model is used for deriving the KdV equation in the long-wave approximation for any dependent variable of the gas-liquid mixture. The KdV equations derived earlier using radically different approximations are particular cases of our equations.