THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION
We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$ , where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonli...
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| Published in | Glasgow mathematical journal Vol. 63; no. 1; pp. 45 - 53 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.01.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0017-0895 1469-509X |
| DOI | 10.1017/S0017089519000491 |
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| Abstract | We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces
${M}^s_{p,q}(\mathbb{R}^d)$
, where q = 1 and
$s\geq0$
or
$q\in(1,\infty]$
and
$s>\frac{d}{q'}$
for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities. |
|---|---|
| AbstractList | We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces
${M}^s_{p,q}(\mathbb{R}^d)$
, where q = 1 and
$s\geq0$
or
$q\in(1,\infty]$
and
$s>\frac{d}{q'}$
for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities. We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$ , where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities. We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces \({M}^s_{p,q}(\mathbb{R}^d)\), where q = 1 and \(s\geq0\) or \(q\in(1,\infty]\) and \(s>\frac{d}{q'}\) for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities. |
| Author | CHAICHENETS, LEONID PATTAKOS, NIKOLAOS |
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| Cites_doi | 10.1007/978-3-7643-8514-9 10.57262/ade/1455805257 10.1142/S021919971450031X 10.2991/jnmp.2008.15.s3.14 10.1080/10652469.2010.541054 10.3934/dcds.2019009 10.1016/0030-4018(94)90560-6 10.5445/IR/1000088173 10.1016/S0764-4442(00)00120-8 10.1016/0022-1236(81)90063-X 10.1103/PhysRevE.53.R1336 10.1016/j.jde.2006.09.004 10.1016/j.jmaa.2013.12.022 10.1007/s00233-019-10016-1 |
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| References | S0017089519000491_ref14 S0017089519000491_ref15 S0017089519000491_ref16 S0017089519000491_ref17 Ben-Artzi (S0017089519000491_ref1) 2000; 330 Karlsson (S0017089519000491_ref8) 1994; 104 Bouchel (S0017089519000491_ref2) 2008; 13 Karpman (S0017089519000491_ref9) 1996; 53 S0017089519000491_ref5 S0017089519000491_ref7 S0017089519000491_ref10 S0017089519000491_ref12 S0017089519000491_ref13 Kato (S0017089519000491_ref11) 2016; 21 Diaz-Ortero (S0017089519000491_ref6) 2008; 15 S0017089519000491_ref4 S0017089519000491_ref3 |
| References_xml | – ident: S0017089519000491_ref13 doi: 10.1007/978-3-7643-8514-9 – volume: 21 start-page: 201 year: 2016 ident: S0017089519000491_ref11 article-title: Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces publication-title: Adv. Differential Equations doi: 10.57262/ade/1455805257 – ident: S0017089519000491_ref3 doi: 10.1142/S021919971450031X – volume: 15 start-page: 137 year: 2008 ident: S0017089519000491_ref6 article-title: Interchannel soliton collisions in periodic dispersion maps on the presence of third order dispersion publication-title: J. Nonlinear Math. Phys. doi: 10.2991/jnmp.2008.15.s3.14 – ident: S0017089519000491_ref16 doi: 10.1080/10652469.2010.541054 – ident: S0017089519000491_ref14 doi: 10.3934/dcds.2019009 – volume: 104 start-page: 303 year: 1994 ident: S0017089519000491_ref8 article-title: Soliton-like pulses governed by fourth order dispersion in optical fibers publication-title: Opt. Commun. doi: 10.1016/0030-4018(94)90560-6 – volume: 13 start-page: 169 year: 2008 ident: S0017089519000491_ref2 article-title: Remarks on NLS with higher order anisotropic dispersion publication-title: Adv. Differential Equ. – ident: S0017089519000491_ref7 – ident: S0017089519000491_ref4 doi: 10.5445/IR/1000088173 – ident: S0017089519000491_ref5 – volume: 330 start-page: 87 year: 2000 ident: S0017089519000491_ref1 article-title: Dispersion estimates for fourth order Schrödinger equations publication-title: C. R. Acad. Sci. Paris, Sér. I Math. doi: 10.1016/S0764-4442(00)00120-8 – ident: S0017089519000491_ref15 doi: 10.1016/0022-1236(81)90063-X – volume: 53 start-page: R1336 year: 1996 ident: S0017089519000491_ref9 article-title: Stabilization of soliton instabilities by higher-order dispersion: Fourth order nonlinear Schrödinger-type equations publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.53.R1336 – ident: S0017089519000491_ref17 doi: 10.1016/j.jde.2006.09.004 – ident: S0017089519000491_ref10 doi: 10.1016/j.jmaa.2013.12.022 – ident: S0017089519000491_ref12 doi: 10.1007/s00233-019-10016-1 |
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| Title | THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION |
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