Novel exact solutions and conserved vectors of the first extended modified (3+1)-dimensional integrable Vakhnenko-Parkes equation

This paper furnished the analytical examination of the first extended modified Vakhnenko-Parkes equation. We computed abundant structures of various exact solutions of this equation through the use of the extended Jacobi elliptic function expansion technique. This approach adopted the use of three different auxiliary nonlinear differential equations to generate the solutions. Thus, we achieved diverse cnoidal, snoida, dnoidal, as well as complex snoidal wave solutions. We further explored the wave dynamics of these periodic solutions in three dimensions and two dimensions using computer software. Moreover, Lie group analysis was utilized to generate the symmetries of the equation. Thereafter, conserved vectors associated to the equation were constructed via the application of Ibragimov's conserved theorem using the formal Lagrangian of the model.