Surface-embeddability approach to the dynamics of the inhomogeneous Heisenberg spin chain

Radha Balakrishnan, Partha Guha

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


The surface-embeddability approach of Lund and Regge is applied to the classical, inhomogeneous Heisenberg spin chain to study the class of inhomogeneity functions f for which the spin evolution equation and its gauge-equivalent generalized nonlinear Schrödinger equation (GNLSE) are exactly solvable. Writing the spin vector S(x,t) as ∂xr and identifying t(x,t) with a position vector generating a surface, we show that the kinematic equation satisfied by r implies certain constraints on the admissible geometries of this surface. These constraints, together with the Gauss-Mainardi-Codazzi equations, enable us to express the coefficient of the second fundamental form as well as f in terms of the metric coefficients G and its derivatives, for arbitrary time-independent G. Explicit solutions for the GNLSE can also be found in terms of the same quantities. Of the admissible surfaces generated by r, a special class that emerges naturally is that of surfaces of revolution: Explicit solutions for r and S are found and discussed for this class of surfaces.

Original languageBritish English
Pages (from-to)3651-3661
Number of pages11
JournalJournal of Mathematical Physics
Issue number8
StatePublished - Aug 1996


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