Abstract
The Akbota equation, as a Heisenberg ferromagnet-type equation, is of great value for the study of the curve and surface geometry. Based on the J-fold Darboux transformation, some novel nonlinear wave solutions such as the one-breather, two-breather, rogue wave and the semi-rational solutions of the Akbota equation are derived. In addition, the corresponding dynamic behaviors of those solutions are discussed via graph simulations.
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