On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow

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3 Citations (Scopus)

Abstract

We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as "Hirota" equation. This equation is a mixture of cubic nonlinear Schrödinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given "modified" free profile by using the two asymptotic formulae for some oscillatory integrals.

Original languageEnglish
Pages (from-to)281-306
Number of pages26
JournalJournal of Differential Equations
Volume245
Issue number2
DOIs
Publication statusPublished - Jul 15 2008
Externally publishedYes

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Korteweg-de Vries equation
Vortex Filament
Axial flow
Asymptotic Behavior of Solutions
Nonlinear equations
Vortex flow
Oscillatory Integrals
Cubic equation
Modified Equations
Korteweg-de Vries Equation
Asymptotic Formula
Global Existence
Nonlinear Equations
Asymptotic Behavior
Tend

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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title = "On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow",
abstract = "We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as {"}Hirota{"} equation. This equation is a mixture of cubic nonlinear Schr{\"o}dinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given {"}modified{"} free profile by using the two asymptotic formulae for some oscillatory integrals.",
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AB - We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as "Hirota" equation. This equation is a mixture of cubic nonlinear Schrödinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given "modified" free profile by using the two asymptotic formulae for some oscillatory integrals.

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