Abstract
Nonlinear equations personate a consequential role in scientific fields such as nonlinear optics, solid state physics and quantum field theory. This article studies the Tzitzeica-Dodd-Bullough-Mikhailov and Tzitzeica-type equations that appear in nonlinear optics. The Painleve and traveling wave transformations both play a key role in revamping the aforementioned equations into nonlinear ordinary differential equations. Then, the simple ansatz approach is followed to seize complex singular, complex bright solitons and other kink type solutions. The existing literature unveils that this study is a novel contribution in the literature and the proposed approach is forthright and simple to implement for solving nonlinear problems. This approach has no extra condition as compared to many other techniques have. We also verify and interpret graphically the secured solutions through symbolic software Mathematica and MatLab respectively.
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