Abstract
An integrable of the generalized Calogero–Bogoyavlenskii–Schiff–Bogoyavlensky–Konopelchenko (CBS–BK) equation is studied, by employing Hirota’s bilinear method the bilinear form is obtained, and the multiple-soliton solutions are constructed. The modified of improved bilinear method has been utilized to investigate multiple solutions. In addition, some graphs including 3D, contour, density, and [Formula: see text]-curves plots of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the linearization solution is analyzed to prove that the modulation instability is stable for some points.
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