On identical traveling-wave solutions of the Kudryashov-Sinelshchikov and related equations

Kudryashov and Sinelshchikov (2010) [2], [3] have developed a one-dimensional theory of the flow of a liquid with gas bubbles. The propagation of waves is described by an evolution equation that contains non-linear terms in the higher derivatives. In the present paper it is shown that traveling-wave solutions of the Kudryashov-Sinelshchikov equation can be found from corresponding solutions of a generalized Korteweg-de Vries equation. Also a new type of periodic waves governed by the KS equation is constructed by gluing together bounded sections of otherwise unbounded solutions of the associated generalized KdV equation.