Multiple soliton solutions and symmetry analysis of a nonlocal coupled KP system

A nonlocal coupled Kadomtsev-Petviashivili (ncKP) system with shifted parity ((P) over cap (x)(s) ) and delayed time reversal (T-d(<^>)) symmetries is generated from the local coupled Kadomtsev-Petviashivili (cKP) system. By introducing new dependent variables which have determined parities under the action of (P) over cap (x)(s) (T) over cap (d)(d) the ncKP is transformed to a local system. Through this way, multiple even number of soliton solutions of the ncKPI system are generated from N-soliton solutions of the cKP system, which become breathers by choosing appropriate parameters. The standard Lie symmetry method is also applied on the ncKPII system to get its symmetry reduction solutions.