Soliton solutions, rational solutions, Matveev solutions, complexitons and mixed solutions for three (2+12+1)-dimension equations

The relations between the consistent solutions to the first two equations of the AKNS hierarchy and the solutions for three (2+12+1)-dimension equations are discussed. Making use of the theory of (1+11+1)-dimension soliton equations and Wronskian technique, soliton solutions, rational solutions, Matveev solutions, complexitons and mixed solutions of the three (2+12+1)-dimension equations are obtained. Specially, the lump-like solutions of the GKPI equation and CKP equation, the periodic solutions of the GKPI equation and the GMKPI equation are also obtained. Besides, the dynamics including one-solitons characteristics, resonances of the two-solitons related to the GKPI equation are investigated analytically.