INTEGRABLE THEORY OF THE PERTURBATION EQUATIONS

An integrable theory is developed for the perturbation equations engen dered from small disturbances of solutions. It includes various integr able properties of the perturbation equations, such as hereditary recu rsion operators, master symmetries, linear representations (Lax and ze ro curvature representations) and Hamiltonian structures, and provides us with a method of generating hereditary operators, Hamiltonian oper ators and symplectic operators starting from the known ones. The resul ting perturbation equations give rise to a sort of integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP equation) a re carefully carried out. Copyright (C) 1996 Elsevier Science Ltd