Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

Abstract The Hirota bilinear method is employed for searching the localized waves, lump–solitons, and solutions between lumps rogue waves fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko (CBS-BK) equation. We probe three cases including lump (combination of two positive functions as polynomial), lump–kink polynomial exponential function) called interaction a one line soliton, lump–soliton hyperbolic cos two-line solitons. At critical point, second-order derivative Hessian matrix only point will be investigated solution has maximum value. moving path also velocity amplitude obtained. graphs various orders ? are plotted to obtain 3D plot, contour density 2D plot. physical phenomena this obtained its soliton analyzed presented in figures by selecting suitable values. That extensively used report many attractive fields fluid dynamics, classical mechanics, physics, so on.