GBDT and algebro-geometric approaches to explicit solutions and wave functions for nonlocal NLS
J. Michor and A.L. Sakhnovich
Keywords: Nonlocal nonlinear Schrödinger equation, explicit solution, wave function, Bäcklund-Darboux transformation, algebro-geometric solution
Abstract: We apply the GBDT version of the Bäcklund-Darboux transforma- tion to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular m1 m2 ma- trix 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.
MSC (2010): 35B06, 35Q55, 14H70, 37K40
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