High-order rational solutions and resonance solutions for a (3+1)–dimensional Kudryashov-Sinelshchikov equation*

Abstract

We mainly investigate the rational solutions and N-wave resonance solutions for the (3+1)-dimensional Kudryashov–Sinelshchikov equation, which could be used to describe the liquid containing gas bubbles. With appropriate transformations, two kinds of bilinear forms are derived. Employing the two bilinear equations, dynamical behaviors of nine district solutions for this equation are discussed in detail, including bright rogue wave-type solution, dark rogue wave-type solution, bright W-shaped solution, dark W-shaped rational solution, generalized rational solution and bright-fusion, dark-fusion, bright-fission, and dark-fission resonance solutions. In addition, the generalized rational solutions, which depending on two arbitrary parameters, have an interesting structure: splitting from two peaks into three peaks.