SYMMETRIES, CONSERVATION-LAWS AND MULTISOLITON PERTURBATION-THEORY

On the basis of action/angle variables for multisolitons, new symmetries (master-symmetries) are constructed. For systems with known hierarchies of non-Hamiltonian mastersymmetries, hierarchies of Hamiltonian mastersymmetries are constructed and for systems with known Hamiltonian mastersymmetries, a hierarchy of non-Hamiltonian mastersymmetries are constructed. Moreover, with the help of the action/angle variables, the N-soliton perturbation theory, on the soliton submanifold (adiabatic approximation), is formulated. An explicit form of the time evolution of asymptotic data under the influence of perturbation is presented.