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dc.contributor.authorHayashi, Nakao ( )
dc.contributor.authorNaumkin, Pavel I. ( )
dc.date.accessioned2020-06-30T16:53:04Z
dc.date.available2020-06-30T16:53:04Z
dc.date.issued2001-07-25
dc.identifier.citationHayashi, N., & Naumkin, P. I. (2001). Asymptotic behaviour for Schrodinger equations with a quadratic nonlinearity in one-space dimension. Electronic Journal of Differential Equations, 2001(54), pp. 1-18.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/11925
dc.description.abstractWe consider the Cauchy problem for the Schr/"{o}dinger equation with a quadratic nonlinearity in one space dimension iut + 1/2 uxx = t -a |ux|2, u (0,x) = u0(x), where α ∈ (0,1). From the heuristic point of view, solutions to this problem should have a quasilinear character when α ∈ (1/2, 1). We show in this paper that the solutions do not have a quasilinear character for all α ∈ [1/2, 1) if the initial data u0 ∈ H3,0 ∩ H2,2 are small, then the solution has a slow time decay such as t -α/2. For α ∈ (0,1/2), if we assume that the initial data u0 are analytic and small, then the small time decay occurs.en_US
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSchrodinger equationen_US
dc.subjectLarge time behaviouren_US
dc.subjectQuadratic nonlinearityen_US
dc.titleAsymptotic Behaviour for Schrodinger Equations with a Quadratic Nonlinearity in One-Space Dimensionen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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