Soliton interaction with small Toeplitz potentials for the Szegö equation on ℝ

Oana Pocovnicu

doi:10.4310/DPDE.2012.v9.n1.a1

Soliton interaction with small Toeplitz potentials for the Szegö equation on ℝ

Oana Pocovnicu^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We consider the cubic Szegö equation with a small Toeplitz potential and with soliton initial data We show that up to time ε ^-1/2 log(1/ε) and errors of size ε ^1/2, the solution preserves the soliton shape u(t, x) = αe ^iφμη(μ(x-a)), and the time dependent parameters a, α, φ, μ evolve according to the effective dynamics, up to small corrections. © 2012 International Press.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Dynamics of Partial Differential Equations
Volume	9
Issue number	1
DOIs	https://doi.org/10.4310/DPDE.2012.v9.n1.a1
Publication status	Published - 2012

Keywords

Effective Hamiltonian
Soliton
Szegö equation
Toeplitz operators

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.4310/DPDE.2012.v9.n1.a1

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abstract = "We consider the cubic Szeg{\"o} equation with a small Toeplitz potential and with soliton initial data We show that up to time ε -1/2 log(1/ε) and errors of size ε 1/2, the solution preserves the soliton shape u(t, x) = αe iφμη(μ(x-a)), and the time dependent parameters a, α, φ, μ evolve according to the effective dynamics, up to small corrections. {\textcopyright} 2012 International Press.",

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AB - We consider the cubic Szegö equation with a small Toeplitz potential and with soliton initial data We show that up to time ε -1/2 log(1/ε) and errors of size ε 1/2, the solution preserves the soliton shape u(t, x) = αe iφμη(μ(x-a)), and the time dependent parameters a, α, φ, μ evolve according to the effective dynamics, up to small corrections. © 2012 International Press.

KW - Effective Hamiltonian

KW - Soliton

KW - Szegö equation

KW - Toeplitz operators

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U2 - 10.4310/DPDE.2012.v9.n1.a1

DO - 10.4310/DPDE.2012.v9.n1.a1

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VL - 9

SP - 1

EP - 27

JO - Dynamics of Partial Differential Equations

JF - Dynamics of Partial Differential Equations

IS - 1

ER -

Soliton interaction with small Toeplitz potentials for the Szegö equation on ℝ

Abstract

Keywords

ASJC Scopus subject areas

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