Breather, lump and X soliton solutions to nonlocal KP equation

Breather, lump and X soliton solutions are presented via the Hirota bilinear method, to the nonlocal (2+1)-dimensional KP equation, derived from the Alice–Bob system. The resulting breather contains two cases, one is the line breather and another is the normal breather, both of which are different from the solutions of the classical (2+1)-dimensional KP equation; the X soliton is found with the long wave limit by some constraints to the parameters; the lump solution is obtained in virtue of two methods, one is as the long wave limit of breather theoretically, the other is with the quadratic function method, which can be guaranteed rationally localized in all directions in the space under some constraints of the parameters. By choosing specific values of the involved parameters, the dynamic properties of some breather, lump solutions to nonlocal KP equation are plotted, as illustrative examples.