Zakharov–Manakov solution of the stimulated Brillouin backscattering generator problem for "spliced" potentials

Making use of the inverse scattering transform method (ISTM), one would like to solve the Zakharov–Manakov (Z–M) problem relevant to nonlinear light scattering for "realistic" nonrectangular input shapes, i.e., shapes which might simulate actual experimental conditions. One approach, which is illustrated in this paper with a specific simple example, is to "splice" potentials together, using potentials for which the Z–M eigenvalue problem is exactly solvable in terms of known functions. A table of such potentials discovered to date is presented. An alternate approach, which avoids splicing, but involves seeking a series solution to the Z–M eigenvalue problem is also briefly discussed.