Novel singular and non-singular complexiton, interaction wave and the complex multi-soliton solutions to the generalized nonlinear evolution equation

The main task of this paper is to plumb some new exact solutions of the (3 + 1)-dimensional generalized nonlinear evolution equation (gNEE) for shallow water waves. In the light of the Hirota method and symbolic computation, a novel ansatz function is proposed to develop the singular complexiton solutions. Meanwhile, the nonsingular complexiton solutions are derived with the introduction of certain constraints. In addition, the interaction wave solutions and the complex multi-soliton solutions are also explored. The profiles of the acquired exact solutions are depicted graphically to exhibit the corresponding physical behaviors. To the best of the authors’ knowledge, the outcomes presented in the work are entirely new and have not been investigated in other literature works, which can extend the exact solutions of the considered equation and enable us to study its nonlinear dynamics better.