Solitons, Surfaces, Curves, and the Spin Description of Nonlinear Evolution Equations
The briefly review on the common spin description of the nonlinear evolution equations.
solv-int↗
arXiv subjects
R. Myrzakulov
Publications and source records attributed to R. Myrzakulov.
A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schrödinger equation introduced by Zakharov and studied recently by Strachan. Using a Hirota bilinearised form, line and curved soliton solutions are obtained. Using certain freedom (arbitrariness) in the solutions of the bilinearised equation, exponentially localized dromion-like solutions for the potential is found. Also, breaking soliton solutions (for the spin variables) of the shock wave type and algebraically localized nature are constructed.
solv-int↗