Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities

Nakao Hayashi; Pavel I. Naumkin

doi:10.3934/ipi.2007.1.391

Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities

Nakao Hayashi, Pavel I. Naumkin

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	391-398
Number of pages	8
Journal	Inverse Problems and Imaging
Volume	1
Issue number	2
DOIs	https://doi.org/10.3934/ipi.2007.1.391
Publication status	Published - 2007
Externally published	Yes

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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10.3934/ipi.2007.1.391

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title = "Modified wave operator for schr{\"O}dinger type equations with subcritical dissipative nonlinearities",

abstract = "We construct the modified wave operator for the nonlinear Schr{\"o}dinger 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.",

keywords = "Asymptotics of solutions, Nonlinear schr{\"o}dinger equations, Subcritical nonlinearities, Wave operators",

author = "Nakao Hayashi and Naumkin, {Pavel I.}",

note = "Funding Information: The work of P.I.N. is partially supported by CONACYT. Publisher Copyright: {\textcopyright} 2007 AIMSciences.",

year = "2007",

doi = "10.3934/ipi.2007.1.391",

language = "English",

volume = "1",

pages = "391--398",

journal = "Inverse Problems and Imaging",

issn = "1930-8337",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Asymptotics of solutions

KW - Nonlinear schrödinger equations

KW - Subcritical nonlinearities

KW - Wave operators

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DO - 10.3934/ipi.2007.1.391

M3 - Article

AN - SCOPUS:34548848638

SN - 1930-8337

VL - 1

SP - 391

EP - 398

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 2

ER -

Modified wave operator for schrÖdinger type equations with subcritical dissipative nonlinearities

Abstract

Keywords

ASJC Scopus subject areas

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