On the theory and numerical simulation of acoustic and heat modes interaction in a liquid with bubbles: acoustic quasi-solitons

摘要

The projecting technique is used to split one-dimensional disturbances into the rightwards progressive, leftwards progressive and stationary modes. Three independent modes are specified by set of orthogonal projectors. The system of coupled nonlinear Korteweg-de Vries (KdV) type equations for the three modes is derived and analysed. The non-singular perturbations method is used to show that for the case of one mode initial excitation the evolution of this mode is approximated by KdV-MKdV (Modified KdV) equation. A version of the numerical Lax-Wendroff (LW) scheme is applied to compute evolution de- scribed by the system. Analytical and numerical evaluations are compared.