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zbMATH Open
Article . 1986
Data sources: zbMATH Open
Transactions of the American Mathematical Society
Article . 1986 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1986 . Peer-reviewed
Data sources: Crossref
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Long Time Asymptotics of the Korteweg-de Vries Equation

Long time asymptotics of the Korteweg-de Vries equation
Authors: Venakides, Stephanos;

Long Time Asymptotics of the Korteweg-de Vries Equation

Abstract

We study the long time evolution of the solution to the Kortewegde Vries equation with initial data υ ( x ) \upsilon (x) which satisfy \[ lim x → − ∞ υ ( x ) = − 1 , lim x → + ∞ υ ( x ) = 0 \lim \limits _{x \to - \infty } \upsilon (x) = - 1,\qquad \lim \limits _{x \to + \infty } \upsilon (x) = 0 \] We show that as t → ∞ t \to \infty the step emits a wavetrain of solitons which asymptotically have twice the amplitude of the initial step. We derive a lower bound of the number of solitons separated at time t t for t t large.

Keywords

Inverse problems for PDEs, inverse scattering method, Partial differential equations of mathematical physics and other areas of application, long time asymptotics, Asymptotic behavior of solutions to PDEs, Korteweg-de Vries equation, Scattering theory for PDEs, wavetrain of solitons, Solitary waves for incompressible inviscid fluids

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
23
Top 10%
Top 10%
Average
bronze