MULTIPLE LOCAL LAGRANGIANS FOR n-COMPONENT SUPER-KORTEWEG DE VRIES-TYPE BI-HAMILTONIAN SYSTEMS

Abstract

The multiple Lagrangian formalism is constructed for n-component Korteweg-de Vries (KdV) type superintegrable systems. They all admit bi-Hamiltonian structure. The first two Lagrangians are local and degenerate. They contain Clebsch potentials for velocity fields and momentum maps in kinetic term. The first local Lagrangian for n-component supermodified KdV (smKdV) is also obtained by employing the multicomponent super-Miura transformation.