Solitons and other solutions for two nonlinear Schrödinger equations using the new mapping method

Zayed and Al-Nowehy have recently employed the extended auxiliary equation method proposed by Xu for finding the solitons and other solutions for two nonlinear evolution equations in mathematical physics, namely the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms and the higher-order dispersive nonlinear Schrödinger equation. In this article, we apply a different method called the new mapping method proposed by Zeng and Yong for constructing many new solitons and other solutions of the same two nonlinear evolution equations mentioned above. Comparing our new solutions of these two evolution equations obtained in this article with the well-known solutions are given. The obtained solutions yielding from these two different methods confirm that they are efficient techniques for analytic treatments of a wide variety of other nonlinear evolution equations.