Geodesic
Cauchy problem for the nonlocal Schr\"odinger equation.~II
Matematičeskoe modelirovanie, Tome 3 (1991) no. 11, pp. 96-109.

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The Cauchy problem for the nonlinear nonlocal Schrödinger equation is studied. The conditions under which discontinuous initial data are smoothing in due course and there exists the solution in the large are found. In the case of untidissipative operators the local in time existence of the classical solutions is proved. 
@article{MM_1991_3_11_a8,
     author = {E. I. Kaikina},
     title = {Cauchy problem for the nonlocal {Schr\"odinger} {equation.~II}},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {96--109},
     publisher = {mathdoc},
     volume = {3},
     number = {11},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1991_3_11_a8/}
}
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E. I. Kaikina. Cauchy problem for the nonlocal Schr\"odinger equation.~II. Matematičeskoe modelirovanie, Tome 3 (1991) no. 11, pp. 96-109. http://geodesic.mathdoc.fr/item/MM_1991_3_11_a8/