Dissipative Model of Nonlinear Waves in Liquid with Gas Bubbles

The two-level dissipative mathematical model of liquid with distributed gas bubbles is created. The numerical and analytical study of nonlinear waves is conducted within the model. A dissipative solitary wave can only exist if there are two pairs of competitive factors, one of which being a balance between weak nonlinearity and dispersion of linear waves and another-balance between the heat flow into a gas medium and that of out of it. Korteweg de Vries equations are derived in long-wave approximation. Compact difference schemes of fourth-order precision are developed for the nonlinear heat conduction equation and generalized heterogeneous wave equation for long-term modeling of wave processes.