Abstract
The nonlinear Schrodinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended $ (\frac{G'}{G^{2}})$ -expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.
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