Abstract
A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti–Leon–Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.
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