## Abstract

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 ∂_{x}r 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 language | British English |
---|---|

Pages (from-to) | 3651-3661 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 37 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1996 |