Abstract
The repulsive nonlinear Schrödinger (NLS) equation with left-right asymmetric boundary conditions is studied by the use of the spectral-transform (ST) techniques. Direct and inverse problems for the associated Dirac operator are extensively treated. With respect to the case of symmetric boundaries the kernel of the Gel’fand-Levitan-Marchenko equation has a new term, which is a truncated Laplace transform of the reflection coefficient. The time evolution of the spectral data is explicitly given and, therefore, the initial-value problem for the NLS equation with asymmetric boundaries is treated in the standard way by the use of the ST.
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