| Summary: | A direct rational exponential scheme is proposed to construct exact multi-soliton solutions and its fission, fusion phenomena after interaction of the solitons has been discussed. We have considered the Burgers and Sharma–Tasso–Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the solitons, respectively. We improve different structured multi-soliton solutions with possible conditions for fission and fusion of the Burgers and the Sharma–Tasso–Olver equations arises in plasma physics and in ocean dynamics. The amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible condition for fission and fusion is proposed. Furthermore, three-dimensional plots of the wave solutions are given to visualize the dynamics of the model.
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