Equivalent Forms of a Generalized Hirota’s Equation with Linear Inhomogeneities

Abstract

A generalized version of the Hirota’s equation with linear inhomogeneities is shown to be equivalent to a generalized continuum Heisenberg ferromagnetic spin chain equation as well as to a generalized Wadati-Konno-Ichikawa-Shimizu (WKIS) type equation, both from geometrical and gauge considerations. The corresponding spectral problems are associated with moving eigenvalues.