Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We construct the modified wave operator for the nonlinear Schrödinger type equations (Formula presented), for (t, x) ∈ R × R. We find the solutions in the neighborhood of suitable approximate solutions provided that β ≥ 2, Im λ > 0 and ρ < 3 is sufficiently close to 3. Also we prove the time decay estimate of solutions (Formula presented). When we prove the existence of a modified scattering operator, then a natural inverse problem arises to reconstruct the parameters β, λ and ρ from the modified scattering operator.

Original languageEnglish
Pages (from-to)391-398
Number of pages8
JournalInverse Problems and Imaging
Volume1
Issue number2
DOIs
Publication statusPublished - 2007
Externally publishedYes

Keywords

  • Asymptotics of solutions
  • Nonlinear schrödinger equations
  • Subcritical nonlinearities
  • Wave operators

ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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