Multiple solitons, soliton molecules, D’Alembert waves, and symmetry analysis for a nonlocal Nizhnik-Novikov-Veselov equation

A nonlocal form of the Nizhnik-Novikov-Veselov (NNV) equation, which is a (2+1)-dimensional extension of the Korteweg-de Vries (KdV) equation, is introduced by employing the consistent correlated bang (CCB) method. By applying the symmetry and anti-symmetry separation method, the nonlocal NNV equation is transformed into a local equation, enabling the derivation of exact solutions from the local counterpart under specific parity and time-reversal constraints. Multiple soliton solutions are constructed via Hirota's bilinear method, and soliton molecules are generated using velocity resonance mechanisms. In addition, a variety of special solutions, including bright and dark-bright solitons, lump waves, and D'Alembert-type waves, are obtained. The Lie symmetry approach is further employed to derive symmetry groups and symmetry reduction solutions.