Computation and observation of novel interaction based on the mixed solutions to a generalized Bogoyavlensky–Konopelchenko equation

Abstract

A generalized Bogoyavlensky–Konopelchenko equation is introduced by using p-generalized bilinear differential operators. The lump solutions, one-lump-one-kink and one-lump-two-kink solutions are derived with symbolic computations. For the two types of mixed solutions, assuming vxand vyrepresent velocities of the kink waves along the x-axis and the y-axis, we find that the velocities of the lump wave and the kink waves along the vector (vx,vy) are equal, while the velocities of the lump wave and the kink waves along the vector (−vy,vx) are not equal. The results imply there is no fission and fusion between the lump wave and the kink waves. The lump wave will not be drowned by kink waves. The results might be helpful to explain the complicated real-world phenomena.

Keywords

• A p-generalized Bogoyavlensky–Konopelchenko equation
• Lump solutions
• Mixed solutions