For the optical soliton model in fifth-order weakly nonlocal nonlinear media, to find its exact explicit solutions, the corresponding traveling wave system is formulated as a planar dynamical system with a singular straight line. Then, by using techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze the planar system and find the corresponding phase portraits, the dynamical behavior of the amplitude component can be assessed. Under different parameter conditions, exact explicit solitary wave solutions, periodic wave solutions, kink, and anti-kink wave solutions, compacton solutions, as well as peakons and periodic peakons are found with precise formulations.
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