SOBOLEV NORMS OF L2-SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION

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SOBOLEV NORMS OF L2-SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION. / Bessonov, R.V.; Denisov, S.A.

In: Pacific Journal of Mathematics, Vol. 331, No. 2, 30.10.2024, p. 217-258.

Research output: Contribution to journal › Article › peer-review

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Bessonov, R.V. ; Denisov, S.A. / SOBOLEV NORMS OF L2-SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION. In: Pacific Journal of Mathematics. 2024 ; Vol. 331, No. 2. pp. 217-258.

BibTeX

@article{bf3b73e155c14bdf885a017ade263084,

title = "SOBOLEV NORMS OF L2-SOLUTIONS TO THE NONLINEAR SCHR{\"O}DINGER EQUATION",

abstract = "We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schr{\"o}dinger equation. For initial datum (Formula presented) and s ∈ [−1, 0], we prove that there exists a conserved quantity which is equivalent to (Formula presented) norm of the solution. {\textcopyright} 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.",

keywords = "Dirac operators, NLSE, scattering, Sobolev norms",

author = "R.V. Bessonov and S.A. Denisov",

note = "Export Date: 18 November 2024 Сведения о финансировании: Russian Science Foundation, RSF, 19-71-30002 Сведения о финансировании: Russian Science Foundation, RSF Сведения о финансировании: National Science Foundation, NSF, DMS-2054465 Сведения о финансировании: National Science Foundation, NSF Текст о финансировании 1: The work of Bessonov in Sections 2 and 3 is supported by the Russian Science Foundation grant 19-71-30002. The work of Denisov in the rest of the paper is supported by the grant NSF DMS-2054465 and Van Vleck Professorship Research Award. Bessonov is a Young Russian Mathematics award winner and would like to thank its sponsors and jury. MSC2020: 35Q55. Keywords: Dirac operators, NLSE, scattering, Sobolev norms.",

year = "2024",

month = oct,

day = "30",

doi = "10.2140/pjm.2024.331.217",

language = "Английский",

volume = "331",

pages = "217--258",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "University of California Press",

number = "2",

}

RIS

TY - JOUR

T1 - SOBOLEV NORMS OF L2-SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION

AU - Bessonov, R.V.

AU - Denisov, S.A.

N1 - Export Date: 18 November 2024 Сведения о финансировании: Russian Science Foundation, RSF, 19-71-30002 Сведения о финансировании: Russian Science Foundation, RSF Сведения о финансировании: National Science Foundation, NSF, DMS-2054465 Сведения о финансировании: National Science Foundation, NSF Текст о финансировании 1: The work of Bessonov in Sections 2 and 3 is supported by the Russian Science Foundation grant 19-71-30002. The work of Denisov in the rest of the paper is supported by the grant NSF DMS-2054465 and Van Vleck Professorship Research Award. Bessonov is a Young Russian Mathematics award winner and would like to thank its sponsors and jury. MSC2020: 35Q55. Keywords: Dirac operators, NLSE, scattering, Sobolev norms.

PY - 2024/10/30

Y1 - 2024/10/30

N2 - We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrödinger equation. For initial datum (Formula presented) and s ∈ [−1, 0], we prove that there exists a conserved quantity which is equivalent to (Formula presented) norm of the solution. © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

AB - We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrödinger equation. For initial datum (Formula presented) and s ∈ [−1, 0], we prove that there exists a conserved quantity which is equivalent to (Formula presented) norm of the solution. © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

KW - Dirac operators

KW - NLSE

KW - scattering

KW - Sobolev norms

UR - https://www.mendeley.com/catalogue/7e0e9e12-1706-379a-9a4c-05066d2330b2/

U2 - 10.2140/pjm.2024.331.217

DO - 10.2140/pjm.2024.331.217

M3 - статья

VL - 331

SP - 217

EP - 258

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -

ID: 127407849