Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer–Kaup system

Abstract

This work reveals a novel phenomenon—that the localized coherent structures of a (2+1)-dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2+1)-dimensional higher-order Broer–Kaup system as a concrete example. Starting from a Backlund transformation, we obtain a linear equation and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.