Analytical Techniques for the Problem of the Interaction of Nonlinear Sonic Waves with Nonuniform Media
Equations describing the propagation of waves with small but finite amplitude in the presence of bubbles with different radii are deduced, keeping account of the dependence of their distribution on space coordinates. The laws of conservation are shown to be significant in choosing the solutions coincident in basic physical properties with the solutions of the initial system. In some particular cases, the equations thus deduced are such known equation as KDV, Kadomtsev-Petviashvily and Khokhlov-Zabolotskaya.
Key wordsNonlinear waves Nonuniform media
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