Identifying Combination of Dark–Bright Binary–Soliton and Binary–Periodic Waves for a New Two-Mode Model Derived from the (2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation

In this paper, we construct a new two-mode model derived from the (2+1)-dimensional Nizhnik–Novikov–Veselov (TMNNV) equation. We generalize concept of Korsunsky to accommodate derivation higher-dimensional equations. Since TMNNV is presented here, for first time, identify some its solutions by means two recent and effective schemes. As result, Kudryashov-expansion method exports combination bright–dark binary solitons, which simulate many applications in optics, photons, plasma. The modified rational sine cosine functions export binary–periodic waves that arise field surface water waves. Moreover, using 2D 3D graphs, physical properties were investigated studying effect following parameters model: nonlinearity, dispersion, phase–velocity. Finally, checked validity obtained verifying correctness original governing model.