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The analytical solutions of the integrable generalized (2+1)-dimensional nonlinear conformable Schrödinger (NLCS) system of equations was explored in this paper with the aid of three novel techniques which consist of (G′/G)-expansion method, generalized Riccati equation mapping method and the Kudryashov method in the conformable sense. We have discovered a new and more general variety of exact traveling wave solutions by using the proposed methods with a variety of soliton solutions of several structures. With several plots illustrating the behavior of dynamic shapes of the solutions, the findings are highly applicable and detailed the physical dynamic of the considered nonlinear system.