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Existence and stability of solitary waves for the inhomogeneous NLS.

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Title: Existence and stability of solitary waves for the inhomogeneous NLS.
Authors: Ramadan, Abba1 (AUTHOR) aramadan@ku.edu, Stefanov, Atanas G.1 (AUTHOR) stefanov@ku.edu
Source: Physica D. Dec2020, Vol. 414, pN.PAG-N.PAG. 1p.
Subjects: Schrödinger equation, Dispersion (Chemistry), Equations
Abstract: In this paper, we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schrödinger equation driven by the subLaplacian dispersion operators (− Δ) s , 0 < s ≤ 1. We construct these waves and we establish sharp asymptotics, both at the singularity 0 and for large values. We show the non-degeneracy of these waves. Finally, we provide spectral and orbital stability classification, under slightly more restrictive assumptions. • We have constructed the solitary waves for the inhomogeneous Sobolev equation, subject to a fractional dispersion. • We have identified necessary and sufficient conditions under which appropriately localized solitary waves exist. • We have classified the stability of solitary waves, for all values of the parameter space. [ABSTRACT FROM AUTHOR]
Copyright of Physica D is the property of Elsevier B.V. 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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DbLabel: Engineering Source
An: 146477485
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Physica+D%22&quot;&gt;Physica D&lt;/searchLink&gt;. Dec2020, Vol. 414, pN.PAG-N.PAG. 1p.
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  Data: In this paper, we identify necessary and sufficient conditions for the existence of appropriately localized waves for the inhomogeneous semi-linear Schr&#246;dinger equation driven by the subLaplacian dispersion operators (− Δ) s , 0 &lt; s ≤ 1. We construct these waves and we establish sharp asymptotics, both at the singularity 0 and for large values. We show the non-degeneracy of these waves. Finally, we provide spectral and orbital stability classification, under slightly more restrictive assumptions. • We have constructed the solitary waves for the inhomogeneous Sobolev equation, subject to a fractional dispersion. • We have identified necessary and sufficient conditions under which appropriately localized solitary waves exist. • We have classified the stability of solitary waves, for all values of the parameter space. [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Physica D is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder&#39;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.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.physd.2020.132691
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Dispersion (Chemistry)
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      – SubjectFull: Equations
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      – TitleFull: Existence and stability of solitary waves for the inhomogeneous NLS.
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              Text: Dec2020
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              Y: 2020
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