Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation

A nonlocal derivative nonlinear Schrödinger equation is discussed. By constructing its Darboux transformations of degree 2n, the explicit expressions of new solutions are derived from zero seed solutions. Usually the derived solutions of this nonlocal equation may have singularities. However, it is shown that the solutions of the nonlocal derivative nonlinear Schrödinger equation can be globally defined and bounded for all (x, t) if the eigenvalues and the parameters characterizing the ratio of the two entries of the solutions of the Lax pair are chosen properly.