We apply the GBDT version of the B\"acklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular $m_1 \times m_2$ matrix functions are dealt with. The wave function is also constructed explicitly. Families of explicit examples are considered in detail. Some initial results and representations for the more complicated algebro-geometric solutions are obtained as well.
Categories: math.AP math-ph math.AG math.MP nlin.SI