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In this work, perturbed Shrödinger equation with Kerr law nonlinearity (p-NSKN) and Kundu-Mukherjee-Naskar (KMN) equation are taken into consideration. New extended algebraic method is applied to get new complex waves for the discussed physical models. Further more, different classes of solitary wave solutions which include dark, dark-singular, dark-bright and singular solutions of type 1 and 2 are reported. Moreover, necessary and sufficient conditions for the existence of the solutions are presented. Graphical representations of some specific solutions with the particular values of parameters are also given. At the end, conclusion is reported.