Exact solutions of the derivative nonlinear Schroedinger equation under the nonvanishing conditions

The inverse method related to a modified Zakharov-Shabat eigen value problem with nonvanishing potentials q(chi) and r(chi), where q(+-infinity)r(+-infinity) = lambda02<>0 is developed. There exists a certain class of the nonlinear evolution equations which are solvable by this method. As the most primitive case a derivative nonlinear Schroedinger equation, iq sub(t) + q sub(xx) - mi(+q+2q)sub(x) = 0(m = -1, +1), is solved under the nonvanishing boundary condition, +q+2 → m lambda02 as x→+-infinity. There appear paired-solitons because of the nonvanishing condition. One paired-soliton solution is obtained with the closed form. This solution shows an algebraic behaviour under a certain limiting condition. (author)