Zakharov-Shabat inverse problem with meromorphic reflection coefficient

Abstract

We analyze the Zakharov-Shabat-type inverse problem when the reflection coefficient contains poles in the eigenvalue plane, as an extension of the earlier work by Atkinson in the case of the Schrodinger problem. It is demonstrated that due to the mutual influence of such a pole and the usual bound-state pole, a discontinuous solitary wave profile is generated. Furthermore, we also examine the form of the nonlinear field only due to the pole of the reflection coefficient. A different approach is necessary to convert the GLM equation into a purely differential one for its solution.