Longwave perturbations in a gas-liquid mixture

Bifurcation analysis and solutions of a three-dimensional Kudryashov–Sinelshchikov equation in the bubbly liquid

“…If v > 0, we have lim h!þ1 u 3 ðhÞ ¼ À 12v 2 25 and lim h!À1 u 3 ðhÞ ¼ 0. Expression (23) corresponds to the heteroclinic orbit in Fig.…”

“…For the unidirectional propagation in the high gas content, the corresponding model is similar to the Korteweg-de Vries (KdV) equation [1]. Further investigation has mentioned that the KdV-Burgers equation can describe the nonlinear water waves with the velocity perturbation in a bubbly liquid [2]. Velocity, pressure and density perturbations of the nonlinear water waves have been investigated with the methods of nonlinear wave dynamics [2].…”

“…Further investigation has mentioned that the KdV-Burgers equation can describe the nonlinear water waves with the velocity perturbation in a bubbly liquid [2]. Velocity, pressure and density perturbations of the nonlinear water waves have been investigated with the methods of nonlinear wave dynamics [2]. Besides, an approximation of the microscopic equations for waves in a bubbly liquid has been derived, the conserved-energy function, sound speed and resonant frequency have been obtained and discussed [3].…”

“…Nonlinear effects on the pressure waves in the bubbly liquids, i.e., the liquids containing gas bubbles inside, have been studied for decades [1,4,3,2,[5][6][7][8][9][10][11]. Four characteristic lengths: wavelength, amplitude, bubble diameter and inter-bubble distance have been discussed [1], whose relative magnitudes affect the dispersion in a bubbly liquid.…”

Extended models of non-linear waves in liquid with gas bubbles

“…If we neglect the liquid compressibility and the interphase heat transfer we obtain the model considered in works [1][2][3][4][5].…”