Abstract
Kudryashov equation describes the propagation pulses in an optical fiber. By using the trial equation method and complete discrimination system for the polynomial method, the classification of all envelope patterns of the Kudryashov equation is obtained, including solitary wave solutions, double periodic solutions, triangular function solutions, and rational function solutions. In particular, the conditions for the existence of each mode are given, and images of the modes are obtained according to the conditions.
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