Abstract
By the Lagrangian multiplier and constraint variational derivative, a relationship between conserved quantities and multi-Hamiltonian structures is built. Using the relation, a method is founded to prove the infinite-dimensional Liouville integrability of evolution equations with continuous variables. As the application, the conservation laws of the Kundu equation are first obtained. Its conserved quantities are deduced for comparing by Fokas' method different from the method used in the existed literature. The integrability of the equation is proved through taking the conservation laws as a starting point.