1 Department of Civil Engineering, Advanced teacher’s training college of the technical education, University of Douala, Douala Cameroon.
2 Department of technology, Faculty of exact and applied science, University of N’djamena, Chad.
3 Department of Mathematics, Physics and Chemistry, Siantou University Institute of Yaoundé, University of Yaoundé 1 Cameroon.
4 Department of Industrial Engineering and Maintenance, Polytechnic University of Mongo, Chad.
2 Department of technology, Faculty of exact and applied science, University of N’djamena, Chad.
3 Department of Mathematics, Physics and Chemistry, Siantou University Institute of Yaoundé, University of Yaoundé 1 Cameroon.
4 Department of Industrial Engineering and Maintenance, Polytechnic University of Mongo, Chad.
Research Article
GSC Advanced Research and Reviews, 2023, 14(01), 095-107.
Article DOI: 10.30574/gscarr.2023.14.1.0378
Received on 23 November 2022; revised on 10 January 2023; accepted on 13 January 2023
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.
2-D discrete NLS equation; 2-D Linear dispersion; 2-D pulse soliton; 2-D pulse compacton
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Fabien Kenmogne, Adoum Kriga, Pierre Marie Wakeu Pola, Adoum Danao Adile and Martial Nde Ngnihamye. 2-D exotic soliton in 2-D Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction. GSC Advanced Research and Reviews, 2023, 14(1), 095-107. Article DOI: https://doi.org/10.30574/gscarr.2023.14.1.0378