Integrability of non-linear differential equations; lax formulation and bi-Hamiltonian structures

Abstract

The integrability of non-linear differential equations are studied on the basis of Lax and bi-Hamiltonian formulations. The relations between the Lax formalism and bi-Hamiltonian structures are analysed and illustrated with well known examples such as the KdV system. Various methods resulting from this analysis are then applied to multicomponent KdV equations.