2024-03-29T08:21:35Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/690162022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Schrdinger Equations with nonlinearity of integral typeHayashi, N.Ozawa, T.open access410We consider the Cauchy problem for the nonlinear Schrodinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. Concerning the problem with finite initial time, we prove the global well-posedness in the largest space L2(!R2 ). Concerning the problem with infinite initial time, we prove the existence of modified wave operators on a dense set of small and sufficiently regular asymptotic states.Department of Mathematics, Hokkaido University1994-10-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83412http://hdl.handle.net/2115/6901610.14943/83412Hokkaido University Preprint Series in Mathematics265212https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69016/1/pre265.pdfapplication/pdf479.11 KB1994-10-01