A (2+1) dimensional integrable spin model: Geometrical and gauge equivalent counterpart, solitons and localized coherent structures

Abstract

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.

14 pages, LaTex, no figures; email of first author: [email protected] and [email protected]

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