A new algorithm for finding Hirota bilinear form (D-Operator) of NPDE?

I need help understanding and implementing an algorithm that has been explained in detail, step by step. While I don’t fully understand the provided code, I can tell that it is likely not very difficult for someone experienced in coding. The algorithm involves substituting terms and working with integrals to derive specific parts of the solution. It seems to handle quadratic and quartic terms and outlines the structure for all dimensions.

Additionally, I believe this method could be used to transform non-linear partial differential equations (NPDEs) into D-operators. There are also many examples available for testing this algorithm, which could be helpful for verifying its correctness.

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https://www.sciencedirect.com/science/article/pii/S2666818122000092