In this article, we will apply the solitary wave ansatz technique and the modified stretched mapping technique to achieve the solitary wave solutions for the cubic-nonlinear Schrödinger equation which describes the slowing varying wave packets and generic small amplitude. The achieved solitary wave solutions using these two distinct techniques will give new visions for the distribution of the ultra-short femtosecond pulses and the rogue wave in optical fiber as well as illustrate the distribution of light in nonlinear optical fibers and planar waveguides. The obtained results which weren’t achieved before via any other authors, who applied various techniques, are new compared with that established previously.
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