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Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches

preprint2018arXivOpen access
J. MichorA. L. Sakhnovich
math.APmath-phmath.MPmath.AGnlin.SI
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Abstract

We apply the GBDT version of the Bäcklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular m1×m2m_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.

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Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches | BZPEER