THE DIRAC INVERSE SPECTRAL TRANSFORM - KINKS AND BOOMERONS

The inverse spectral transform (IST) is derived when using the eigenvalue problem for the one-dimensional Dirac operator: (D) = iσ3(d/dx) + i(r ∼0 0 -q∼), σ3 = (0 1 -1 0), where the potentials q∼ and r∼ have nonzero asymptotic values. The method used is of AKNS type. It is shown that the nonlinear evolution equations (NEE) obtained are of differential type at any order (and not of integro-differential type). Some particular solutions are studied, and it is shown that their special behavior is a direct consequence of the nonzero boundary condition on (D). © 1980 American Institute of Physics.