Fractal structure of ferromagnets: The singularity structure analysis

摘要

Following the Weiss-Tabor-Carnevale approach [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984).] designed for studying the integrability properties of nonlinear partial differential equations, we investigate the singularity structure of a (2+1)-dimensional wave-equation describing the propagation of polariton solitary waves in a ferromagnetic slab. As a result, we show that, out of any damping instability, the system above is integrable. Looking forward to unveiling its complete integrability, we derive its B¨acklund transformation and Hirota’s bilinearization useful in generating a set of soliton solutions. In the wake of such results, using the arbitrary functions to enter into the Laurent series of solutions to the above system, we discuss some typical class of excitations generated from the previous solutions in account of a classification based upon the different expressions of a generic lower dimensional function. Accordingly, we unearth the nonlocal excitations of lowest amplitudes, the dromion and lump patterns of higher amplitudes, and finally the stochastic pattern formations of highest amplitudes, which arguably endow the aforementioned system with the fractal properties.