Abstract
An effect of the liquid viscosity and the thermal conductivity and nonuniform distribution of initial flow velocity on weakly nonlinear propagation of pressure waves in an initially quiescent liquid containing many small spherical gas bubbles is theoretically elucidated. Based on the derivation of the KdV–Burgers equation for a long wave and the nonlinear Schrodinger equation for a short carrier wave, the following results are obtained: (i) the installation of the energy equation affects nonlinear, dispersion, and dissipation effects; (ii) the liquid viscosity and the thermal conductivity lead to change considerably the explicit form of the coefficient in the dissipation term; and (iii) the weak nonuniform effect appears in a far field.
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