%0 Journal Article %1 fabien_kenmogne_2023_7678484 %A Kenmogne, Fabien %A Kriga, Adoum %A Pola, Pierre Marie Wakeu %A Adile, Adoum Danao %A Ngnihamye, Martial Nde %D 2023 %J GSC Advanced Research and Reviews %K 2-D NLS discrete equation %N 1 %P 095-107 %R 10.30574/gscarr.2023.14.1.0378 %T 2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction %U https://gsconlinepress.com/journals/gscarr/content/2-d-exotic-soliton-2-d-heisenberg-ferromagnetic-chains-dzyaloshinsky-moriya-interaction %V 14 %X 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.

@article{fabien_kenmogne_2023_7678484, 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.}, added-at = {2023-03-03T09:34:17.000+0100}, author = {Kenmogne, Fabien and Kriga, Adoum and Pola, Pierre Marie Wakeu and Adile, Adoum Danao and Ngnihamye, Martial Nde}, biburl = {https://www.bibsonomy.org/bibtex/2bdfe3f5481e0c19de8b414ebdc78e4e6/gscarrjournal}, doi = {10.30574/gscarr.2023.14.1.0378}, interhash = {299d5c307c03c2ce0e0c9d3a9e090199}, intrahash = {bdfe3f5481e0c19de8b414ebdc78e4e6}, issn = {2582-4597}, journal = {GSC Advanced Research and Reviews}, keywords = {2-D NLS discrete equation}, month = jan, number = 1, pages = {095-107}, timestamp = {2023-03-03T09:34:17.000+0100}, title = {2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction}, url = {https://gsconlinepress.com/journals/gscarr/content/2-d-exotic-soliton-2-d-heisenberg-ferromagnetic-chains-dzyaloshinsky-moriya-interaction}, volume = 14, year = 2023 }