Asymptotic Behaviour for Schrodinger Equations with a Quadratic Nonlinearity in One-Space Dimension

Simple item page
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.description.abstractWe consider the Cauchy problem for the Schrödinger equation with a quadratic nonlinearity in one space dimension iut + 1/2 uxx = t-α |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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHayashi, N., & Naumkin, P. I. (2001). Asymptotic behaviour for Schrodinger equations with a quadratic nonlinearity in one-space dimension. <i>Electronic Journal of Differential Equations, 2001</i>(54), pp. 1-18.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/11925
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSchrodinger equation
dc.subjectLarge time behaviour
dc.subjectQuadratic nonlinearity
dc.titleAsymptotic Behaviour for Schrodinger Equations with a Quadratic Nonlinearity in One-Space Dimension
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
hayashi.pdf
Size:
295.72 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Journal of Differential Equations