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New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation.

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Title: New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation.
Authors: Getachew, Tegegne1 (AUTHOR) gcmsc2006@gmail.com, Shi, Xiasheng1 (AUTHOR) shixiasheng@zju.edu.cn
Source: Journal of Applied Mathematics. 7/6/2026, Vol. 2026, p1-9. 9p.
Subjects: Nonlinear Schrödinger equation, Analytic functions, Initial value problems, Mathematical analysis, Gevrey class, Sobolev spaces, Conservation laws (Physics)
Abstract: In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in the spatial variable. We show the uniform radius of spatial analyticity σ(T) of solutions at time T cannot decay faster than cT−2 for large T. This improves a recent result by Figueira and Panthee, where they established a decay rate of order cT−(4 + ε) for ε > 0. We used an approximate conservation law in the modified Gevrey spaces, a contraction mapping argument, space‐time estimates and one‐dimensional Sobolev embedding to obtain our improved result. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 7/6/2026, Vol. 2026, p1-9. 9p.
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  Label: Abstract
  Group: Ab
  Data: In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in the spatial variable. We show the uniform radius of spatial analyticity σ(T) of solutions at time T cannot decay faster than cT−2 for large T. This improves a recent result by Figueira and Panthee, where they established a decay rate of order cT−(4 + ε) for ε > 0. We used an approximate conservation law in the modified Gevrey spaces, a contraction mapping argument, space‐time estimates and one‐dimensional Sobolev embedding to obtain our improved result. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1155/jama/2851779
    Languages:
      – Code: eng
        Text: English
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        PageCount: 9
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    Subjects:
      – SubjectFull: Nonlinear Schrödinger equation
        Type: general
      – SubjectFull: Analytic functions
        Type: general
      – SubjectFull: Initial value problems
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
      – SubjectFull: Gevrey class
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      – SubjectFull: Sobolev spaces
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      – SubjectFull: Conservation laws (Physics)
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      – TitleFull: New Lower Bounds on the Radius of Spatial Analyticity for the Third‐Order Nonlinear Schrödinger Equation.
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            NameFull: Getachew, Tegegne
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            NameFull: Shi, Xiasheng
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            – D: 06
              M: 07
              Text: 7/6/2026
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              Y: 2026
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