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Modal Expansions and Completeness Relations for Some Time-Dependent Schrödinger Equations

P. D. Miller and N. N. Akhmediev
Australian Photonics Cooperative Research Centre
Optical Sciences Centre
Research School of Physical Sciences and Engineering
The Australian National University, Canberra ACT 0200 Australia


With the use of a variant of the method of separation of variables, the initial value problem for the time-dependent linear Schrödinger equation is solved exactly for a large class of potential functions related to multisoliton interactions in the vector nonlinear Schrödinger equation. Completeness of states is proved for absolutely continuous initial data in L1.