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