A New Nonlinear Integrable Couplings of GJ Equations Hierarchy and Its Hamiltonian Structure

Abstract

In this paper, based on the rudimentary knowledge of the nonlinear integrable couplings, we establish a scheme for constructing nonlinear integrable Hamiltonian couplings of soliton hierarchy. Variational identities over the corresponding loop algebras are used to offer Hamiltonian structures for the resulting continuous couplings. As an application, we use this method to obtain a nonlinear integrable couplings and Hamiltonian structure of the GJ hierarchy by using Tu scheme and the quadratic-form identity.KeywordsZero curvature equationsIntegrable couplingsThe GJ hierarchy