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 y-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.

中文翻译：

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广义 CBS-BK 方程的调制不稳定性和多重流氓波解

研究了广义Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko(CBS-BK)方程的可积，采用Hirota的双线性方法得到双线性形式，并构造了多孤子解。改进的双线性方法已被用于研究多个解决方案。此外，一些图形包括 3D、等高线、密度和是的显示了具有特定系数的所寻址方程的曲线图。最后，在一定条件下，分析了线性化解的渐近行为，证明调制不稳定性对于某些点是稳定的。