Pressure wave characteristics in a bubble-liquid mixture via Kudryashov–Sinelshchikov equation

Abstract

The general solutions for nonlinear waves in a bubble-liquid mixture are obtained from the Kudryashov–Sinelshchikov (KS) equation under different parametric regimes. The Chiellini integrability condition has been used for constructing exact general solutions. In the non-dissipative case, we find that the solutions may be expressed in terms of Jacobi elliptic and Weierstrass functions. On the other hand, in the dissipative case, only implicit solutions are obtained for the KS equation. For an alternative perspective, the notion of the Jacobi Last Multiplier has been utilized to obtain the corresponding Lagrangian and Hamiltonian description of the reduced equation for the bubble-liquid mixture system.

Keywords:

• Pressure waves
• bubble-liquid mixture
• Kudryashov–Sinelshchikov equation
• traveling waves
• Cheillini condition
• Jacobi elliptic function

Mathematics Classifications (2010):

• 34C14
• 34C20

Disclosure statement

No potential conflict of interest was reported by the author(s).