Dispersion-Driven Lump Waves in a (2+1)-Dimensional Generalized Bogoyavlensky-Konopelchenko-like Model

Abstract This study investigates dispersion-induced lump wave structures in a generalized Bogoyavlensky-Konopelchenko-type model in (2+1)-dimensions. A generalized bilinear representation of the governing equation is first established using generalized bilinear derivatives with $$p=3$$ . Positive quadratic wave solutions are then derived via symbolic computation, which in turn generate lump-type wave structures. Our analysis reveals that the stationary points of these quadratic waves lie on a straight line in the spatial plane and propagate with constant velocities. Along this characteristic trajectory, the lump amplitude vanishes. The emergence of these lump structures is attributed to the interplay between nonlinear and dispersive effects in the model.