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In this paper, the double (G'/G, 1/G)-expansion method is employed to establish explicit general solutions of the nonlinear (2 + 1)-dimensional soliton equation. A variety of exact travelling wave solutions are attained involving three functions that are classified into rational, trigonometric and hyperbolic with especial parameters that originate the solitary explicit and new periodic solutions. The used method is the generalization of the (G'/G)-expansion method and it rediscovers all the acquainted solitary wave solutions that are obtained by means of the (G'/G)-expansion method.