Lump-Wave Structures in an Extended KP-like Model with Spatially Balanced Nonlinearity and Dispersion

Abstract This study investigates lump-wave structures arising from the interaction between nonlinear and dispersive effects in an extended KP-like nonlinear model with spatially balanced nonlinearity and dispersion in $$(2+1)$$ ( 2 + 1 ) dimensions. Using generalized bilinear derivatives associated with the prime number three, a generalized bilinear form is first proposed, from which a nonlinear model equation with spatially balanced nonlinearity and dispersion is derived. By employing symbolic computation in Maple, positive quadratic wave solutions are constructed, giving rise to localized lump-wave structures. It is shown that the stationary points of the quadratic waves lie on a straight line in the spatial plane and propagate with constant velocity. Along the trajectory of these stationary points, the lump waves maintain constant amplitude. The novelty of this work lies in the application of generalized bilinear derivatives associated with the prime number three. The results demonstrate that the formation of lump waves is fundamentally governed by the combined effects of nonlinearity and dispersion within the model.