The generation mechanism of rouge wave for (3 + 1)-dimensional Kudryashov–Sinelshchikov equation

In this paper, the rational form of the high-order rogue wave can be derived from the N -soliton solutions of (3 + 1)-dimensional Kudryashov–Sinelshchikov equation. Specifically, these higher-order rogue wave solutions are obtained by making a subtle perturbation to the phase parameters of the soliton. Furthermore, various patterns of the rogue wave such as the fundamental pattern, triangular pattern and pentagonal pattern can be obtained. In addition, some dynamical behaviors of rogue wave are proposed. This generation mechanism can also be applied to other integrable systems.