LAUSR

Abstract In this study, a significant model of mathematical physics used to describe real-world problems, namely the Nizhnik–Novikov–Veselov (NNV) system is studied and various versions of wave solutions are simultaneously explored. The NNV system is considered an essential model to the KdV hierarchy and is widely used to study the scalar nucleons associated with neutral scalar masons. Thus, the exact wave solutions are important to the associated researchers. To this aim, a robust approach named the generalized exponential rational function method (GERFM) is used to achieve this goal. With the aid of GERFM abundant new wave solutions are formally constructed. All generated solutions are constructed with distinct forms that are dependent on free parameters and determined by the self-form of the NNV system. Moreover, the free parameters play the main roles in the dispersive terms and the values of free parameters influence the physical properties of the traveling solitary and periodic waves to the NNV system directly. Finally, some 3D graphs of the generated solutions are provided to show the propagations of traveling waves. The performed results will have great potential applications to optical fibers, magneto-electrodynamics, the collision of heavy ions, and quantum mechanics.