On the Solutions for a Fifth Order Kudryashov–Sinelshchikov Type Equation

Abstract

The fifth order Kudryashov–Sinelshchikov equation models the evolution of the nonlinear waves in a gas–liquid mixture, taking into account an interphase heat transfer, surface tension, and weak liquid compressibility simultaneously at the derivation of the equations for non-linear-waves. We prove the well-posedness of the solutions for the Cauchy problem associated with this equation for each choice of the terminal time T.