Abstract: Background and Objective: The nonlinear Schrödinger equation plays an important role in Physics and Applied Mathematics as well. The analysis of structures of the Schrödinger equation has gained considerable momentum and a particular attention. This study aimed to use the symbolic solutions via the differential transform approach. Methodology: Through differential transform method, some exact and approximate traveling wave solutions of linear and nonlinear Schrödinger equations are investigated. Results: Miscellaneous traveling wave solutions including, exponential solutions are obtained. On one side, for the first case study, two exact expressions of solutions for the linear case are obtained with the iterated sequence. On the other side, for the second case study, four exact expressions of solutions for the nonlinear case have been computed exactly as in the linear case. Conclusion: Some examples are examined, with different physical structures to show the real power of the proposed method. Through computational aspects, this approach can successfully ensure the convergence of true solutions and gives new results under a symbolic aspect.