The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky–Konopelchenko (BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point, the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He’s semi-inverse variational principle (SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values. This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.

中文翻译：

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流体力学中的Hirota双线性和SIVP格式的广义BK方程的多重流浪和孤立解

为了获得广义Bogoyavlensky-Konopelchenko（BK）方程的多个孤子解，采用了多重团解法。获得的解包含一阶，二阶和三阶波动解。在临界点，仅研究了一个点的二阶导数和Hessian矩阵，并且整块解具有一个最大值。他的半逆变分原理（SIVP）也用于广义BK方程。基于使用SIVP的两种不同分析，研究了三个主要案例。然后，通过选择合适的参数值，对由此获得的多个孤子溶液的物理现象进行分析并在下图中进行演示。