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| Nonlinear Schrodinger (NLS) equations are universal models for the evolution of weakly nonlinear dispersive wave trains which are also completely integrable, infinite-dimensional Hamiltonian systems. Despite having been intensely investigated over the last forty years, these systems still offer a number of challenges, some of these involve the study problems in which non-zero boundary conditions (NZBC) are given. This talk with discuss a number of recent results in this area. In particular, I will discuss the solution of both focusing and defocusing, scalar and vector NLS equations with NZBC. A number of explicit soliton solutions will be discussed, as well as spectral problems for special classes of initial conditions. |
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