The complete symmetry group of the generalised hyperladder problem

Abstract

We further consider the n-dimensional ladder system, that is the homogeneous quadratic system of first-order differential equations of the form x ̇ i=x i∑ j=1 na ijx j , i=1, n, where ( a ij )=( i+1− j), i, j=1, n introduced by Imai and Hirata ( nlin.SI/0212007). We establish the most general system of first-order ordinary differential equations invariant under the algebra which characterises the ladder system of Imai and Hirata and the algebra of minimal dimension required to specify completely this most general system. We provide the complete symmetry group of the generalised hyperladder system and discuss its integrability.