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A Search Method for Hirota Bilinear Systems of Nonlinear Evolution Equations
I. Albazlamit, L. Al Sakkaf, U. Al Khawaja
https://arxiv.org/abs/2508.15590 https://

A Search Method for Hirota Bilinear Systems of Nonlinear Evolution Equations
We present a systematic search method for finding Hirota bilinear systems of nonlinear evolution equations, with emphasis on the nonlinear Schrödinger equation (NLSE). Using a known exact solution, couplings between the different terms of the differential equation are identified, which are then used to derive the bilinear system. We show that a nonlinear evolution equation may have many solution-dependent Hirota bilinear systems. Nonetheless, all solution members of a certain solution class ar…