“…e role of nonlinearity in waves is quite signi cant, mostly throughout non-linear sciences; research development towards exact solutions of partial di erential nonlinear equations has always been a major endeavor for the past couple of years. All the while, several powerful, e cient, and reliable methods for attempting to seek exact analytical solutions to traveling waves have been established: for example, the N-soliton solution [7], a fractional-order multiple-model type-3 fuzzy control [8], a calculation methodology for geometrical characteristics [9], a combination of group method of data handling and computational uid dynamics [10], the truss optimization with metaheuristic algorithms [11], the extended generalized Darboux method [12], the Lax pair technique [13], intermolecular interactions to the modern acid-base theory [14], the deep learning for Feynman's path integral [15], the Darboux-Bäcklund technique [16], the Hirota bilinear technique [17], the multiple exp-function method [18], optimal structure design [19], the experimental study on circular steel [20,21], an influence of seismic orientation on the statistical distribution [22], effects of actual loading waveforms on the fatigue behaviors [23], and so on [24][25][26][27]. Hirota bilinear method is an efficient instrument to construct exact solutions of NLEEs, and there exist a lot of completely integrable equations that are investigated in this procedure, for example, the generalized bilinear equations [28], the Kadomtsev-Petviashvili (KP)-Benjamin-Bona-Mahony equation [29], the optimal Galerkin-homotopy asymptotic method [30], the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation [31], the KP equation [32], the B-type KP equation [33], the optical interactions within magnetic layered structures [34], the (2 + 1)dimensional breaking soliton equation [35], and the bidirectional Sawada-Kotera equation …”