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Density waves in the full velocity difference model. (English) Zbl 1093.82012

The authors investigate density waves in the full velocity difference model (FVDM) analytically and numerically. By use of nonlinear analysis, they derive the Burgers, Korteweg-de Vries (KdV) and Modified KdV equations for the triangular shock wave, the soliton wave and the kink-antikink wave. They show numerically, that the triangular shock wave and the soliton wave are determined by the initial perturbation configuration and that different initial perturbations will produce different wave forms.

MSC:

82B99 Equilibrium statistical mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
35Q53 KdV equations (Korteweg-de Vries equations)
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