摘要
In this research,invariant subspaces and exact solutions for the governing equation are obtained through the invariant subspace method,and the generalized second-order Kudryashov-Sinelshchikov equation is used to describe pressure waves in a liquid with bubbles.The governing equations are classified and transformed into a system of ordinary differential equations,and the exact solutions of the classified equation are obtained by solving the system of ordinary differential equations.The method gives logarithmic,polynomial,exponential,and trigonometric solutions for equations.The primary accomplishments of this work are displaying how to obtain the exact solutions of the classified equations and giving the stability analysis of reduced ordinarydifferential equations.
基金
supported by a training program for key young teachers of colleges and universities in Henan Province(No.2019GGJS143)
the Natural Science Foundation of Shannxi Province of China(No.2021JM-521)
key research projects of Henan higher education institutions(No.21A110026)
research team development project of Zhongyuan University of Technology(No.K2020TD004)
the Natural Science of Foundation of Zhongyuan University of Technology(No.K2023MS002).
