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

Abstract

A non-isospectra (2 + 1)-dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts are the (2 + 1)-dimensional non-linear Schrodinger equation belonging to the class of equations discovered by Calogero and then discussed by Zakharov and studied recently by Strachan. Using a Hirota bilinearized form, line and curved soliton solutions are obtained. Using a certain freedom (arbitrariness) in the solutions of the bilinearized equation, exponentially localized dromion-like solutions for the potential are found. Also, breaking soliton solutions (for the spin variables) of shock wave type and algebraically localized nature are constructed.