Soliton-M-lump wave formation and other interacting propagation for the nonlinear Geng equation

Abstract

In this work, we obtain various kind of lump interaction solutions for the (3 + 1)-dimensional nonlinear Geng equation, which was derived in relation to Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobian. The well-known technique namely Hirota bilinear is used to accomplish the task. A lump solution is a real analytical rational function solution that decays in all directions of the space variables. The governing equation describes wave dynamical behaviors in more complex applications related to shallow water wave or other similar fluids. Numerical simulations using the three-dimensional and contour profiles are carried out with careful consideration for the values of the involved parameters in order to shed more light on the properties of the acquired solutions.