Global Behavior of Solutions to Generalized Gross-Pitaevskii Equation

This paper is concerned with time global behavior of solutions to nonlinear Schrödinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing s...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 32; no. 3; pp. 743 - 761
Main Authors Masaki, Satoshi, Miyazaki, Hayato
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 2024
Springer Nature B.V
Subjects
Computer Science
Engineering
Mathematics
Mathematics and Statistics
Nonlinearity
Original Research
Schrodinger equation
Non-vanishing boundary condition
Scattering
35P25
Gross-Pitaevskii equation
35Q55
Nonlinear Schrödinger equations
35B40
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Summary:This paper is concerned with time global behavior of solutions to nonlinear Schrödinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing state. To observe this phenomenon, we introduce a generalized version of the Gross-Pitaevskii equation, which is a typical equation involving a non-vanishing condition, by modifying the shape of nonlinearity around the non-vanishing state. It turns out that, if the nonlinearity decays fast as a solution approaches to the non-vanishing state, then the equation admits a global solution which scatters to the non-vanishing element for both time directions.
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-022-00609-8