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

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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 μη(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 languageEnglish
Pages (from-to)1-27
Number of pages27
JournalDynamics of Partial Differential Equations
Volume9
Issue number1
DOIs
Publication statusPublished - 2012

Keywords

  • Effective Hamiltonian
  • Soliton
  • Szegö equation
  • Toeplitz operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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