Lump waves in a generalized Bogoyavlensky-Konopelchenko model with spatially balanced derivatives

This paper investigates lump waves in a generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko model with spatially balanced derivatives. Using a sum-of-squares ansatz, symbolic computation in Maple is employed to construct lump wave solutions of the nonlinear model from positive quadratic functions. The interplay of four sets of nonlinear terms and five dispersion terms gives rise to the resulting lump waves. The critical points of these quadratic functions are determined, and they travel at constant velocities along a straight line in the spatial plane. Along this characteristic line, the constructed lump waves remain invariant. Concluding remarks are provided in the final section.