Finite-band solutions of the Dirac soliton equation through a reduction technique

Abstract

A nonlinearization technique is used to split the 1+1 dimensional soliton equation into two compatible Hamiltonian systems of ordinary differential equations in the finitedimensional invariant set of the flow. The Dirac soliton hierarchy, with the defocusing nonlinear Schrodinger equation as one of its member, is investigated in detail to illustrate the technique. A numerical example is given.