Nonlinear dynamics of specific physical waves of a (2+1)-dimensional generalized Sawada–Kotera equation

In this paper, a [Formula: see text]-dimensional generalized Sawada–Kotera (2D-gSK) equation, with significant applications in quantum gravity field theory, is explored. The study begins by bilinearizing the 2D-gSK equation using the Bell polynomial (BP) method and continues by finding its multiple solitons, after verifying integrability properties, through the simplified Hirota method. Some theorems regarding the existence of multi-lump waves are formally presented as direct results of multiple solitons. To complete the studies, some other specific nonlinear waves of the 2D-gSK equation, such as breather, complexiton, and Jacobi waves, are constructed in a detailed manner. In the end, as a result of the multidimensional and density representations, the dynamic features of such nonlinear waves are assessed. This work provides valuable results regarding nonlinear waves of the 2D-gSK equation and their dynamics.