Abstract
The present study emphasis to look for new closed form exact solitary wave solutions for the $$(n+1)$$ -dimensional nonlinear Schrodinger equation using the extended trial equation method (ETEM) and the $$\exp (-\Omega (\eta ))$$ -expansion method (EEM) with the help of symbolic computation package maple. As a consequence, the ETEM and EEM are successfully employed and acquired some new exact solitary wave solutions in terms of exponential based functions, hyperbolic based functions, trigonometric based functions and rational based functions. All solutions have been verified back into its corresponding equation with the aid of maple package program. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in the field of nonlinear optic.
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