2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction

The two-dimensional (2D) version of ferromagnet XXZ spin chain with DzyaloshinskyMoriya (DM) interaction, recently introduced by F. Kenmogne and coworkers is reexplored. Firstly using the Dyson-Maleev transformation, 2-D discrete nonlinear Schrödinger (DNLS) equation, governing quantum states behaviors found. Next semidiscrete multiple-scale method, DNLS equation reduced to 2D extended (ENLS) which consists basic NLS additional dispersive terms. This admits classical pulse states, when terms vanish. In addition, this compacton peakon-like boson states. Furthermore, we notice that on contrary outcomes where amplitudes both solutions are free parameters, for two dimensional not parameters since obtained need be normalized.