The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation

Abstract The aim of this work is to explore the excitation of high-order localized waves in the (3+1)-dimensional Kudryashov-Sinelshchikov equation, which is used to describe the dynamic of liquid with gas bubble. First of all, classical N -soliton solutions are constructed by means of Hirota bilinear form and symbolic calculation. What’s more, the high-order breather waves are derived through the degeneration process of the N -soliton solutions with conjugate parameter. Then, high-order lump waves are constructed by taking long wave limit technique on N -soliton solutions. Finally, the high-order mixed localized waves involving resonant Y -type solitons, high-order breather waves and high-order lump waves are obtained by utilizing some comprehensive methods. Abundant dynamical and evolutionary behaviors of these results are investigated specifically, some figures are presented to shed light on the nonlinear phenomena hidden in the high-order localized waves vividly.