Bright and dark soliton solutions to the partial reverse space–time nonlocal Mel’nikov equation

General bright and dark soliton solutions to the partial reverse space–time nonlocal Mel’nikov equation with parity–time symmetry are constructed by the Hirota bilinear method with KP hierarchy reduction method. These solutions of arbitrary order are given in forms of Gram-type determinants. The properties of propagation and collision of analytical solution including both bright and dark solitons are discussed in details. In the end, we provide a simple variable transformation to convert the nonlocal Mel’nikov equation to a local Mel’nikov equation.