Abstract
In this article, the first and second-order rogue wave solutions are obtained which are localized in both space and time that appear from nowhere and disappear without a trace. The coupled NLSEs with time-dependent coefficients are considered that describe the effects of ultrashort optical pulse propagation in nonlinear optics and quantum physics. The similarity transformation is used to investigate these rational-like (rogue wave) solutions. Moreover, the 3D graphical representations and contour plots have depicted with different parameters of gravity field and external magnetic field.
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