Localized Wave and Other Special Wave Solutions to the (3 + 1)‐dimensional Kudryashov–Sinelshchikov Equation

ABSTRACT

This paper aims to explore some different localized wave solutions to the (3 + 1)‐dimensional Kudryashov–Sinelshchikov equation (KSe) for the liquid with gas bubbles. First, the traveling wave transformation is employed to reduce the dimension of the (3 + 1)‐dimensional KSe. Then the Hirota bilinear method is adopted to develop the rogue wave solutions via introducing the different polynomial functions. By optimizing the parameters, the bright and dark rogue waves solutions of the first‐order and second‐order are extracted. In addition, the three‐wave method is employed to seek the generalized breathers wave, W‐shape (double well or breather wave), bright and dark solitary wave solutions. Besides, the other special wave solutions like the compacton and singular wave solutions are also reported. Meanwhile, the dynamic attributes of some solutions are unfolded by Maple. To the best of the authors' knowledge, the findings of this research are all new and have not explored in other literature.