Periodic Loop Solutions and Their Limit Forms for the Kudryashov-Sinelshchikov Equation

A mixture of liquid and gas bubbles of the same size may be considered as an example of a classic nonlinear medium. In practice, analysis of propagation of the pressure waves in a liquid with gas bubbles is important problem. We know that there are solitary and periodic waves in a mixture of a liquid and gas bubbles and these waves can be described by nonlinear partial differential equations. As for examples of nonlinear differential equations to describe the pressure waves in bubbly liquids, we can point out the Burgers equation, the Korteweg-de Vries equation, the Burgers-Korteweg-de Vries equation, and so on 1 . In 2010, Kudryashov and Sinelshchikov 1 obtained amore common nonlinear partial differential equation for describing the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer, and the equation reads as follows: