Solutions of mKdV in classes of functions unbounded at infinity

T. Kappeler; P. Perry; M. Shubin; P. Topalov

doi:10.1007/s12220-008-9013-3

Solutions of mKdV in classes of functions unbounded at infinity

T. Kappeler, P. Perry, M. Shubin, P. Topalov

Mathematics

Producción científica: Article › revisión exhaustiva

11 Citas (Scopus)

Resumen

Using P. Lax's concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.

Idioma original	English
Páginas (desde-hasta)	443-477
Número de páginas	35
Publicación	Journal of Geometric Analysis
Volumen	18
N.º	2
DOI	https://doi.org/10.1007/s12220-008-9013-3
Estado	Published - abr 2008

Nota bibliográfica

Funding Information:
T. Kappeler supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652). P. Perry partially supported by NSF-grant DMS-0408419. M. Shubin partially supported by NSF-grant DMS-0600196.

Financiación

T. Kappeler supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652). P. Perry partially supported by NSF-grant DMS-0408419. M. Shubin partially supported by NSF-grant DMS-0600196.

Financiadores	Número del financiador
European Community
NSF-grant	DMS-0600196, DMS-0408419
Marie Curie	MRTN-CT-2004-5652
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-008-9013-3

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abstract = "Using P. Lax's concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.",

keywords = "KdV, Modified KdV, Spectra of Schr{\"o}dinger operators",

author = "T. Kappeler and P. Perry and M. Shubin and P. Topalov",

note = "Funding Information: T. Kappeler supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652). P. Perry partially supported by NSF-grant DMS-0408419. M. Shubin partially supported by NSF-grant DMS-0600196.",

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T1 - Solutions of mKdV in classes of functions unbounded at infinity

AU - Kappeler, T.

AU - Perry, P.

AU - Shubin, M.

AU - Topalov, P.

N1 - Funding Information: T. Kappeler supported in part by the Swiss National Science Foundation, the programme SPECT, and the European Community through the FP6 Marie Curie RTN ENIGMA (MRTN-CT-2004-5652). P. Perry partially supported by NSF-grant DMS-0408419. M. Shubin partially supported by NSF-grant DMS-0600196.

PY - 2008/4

Y1 - 2008/4

N2 - Using P. Lax's concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.

AB - Using P. Lax's concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.

KW - KdV

KW - Modified KdV

KW - Spectra of Schrödinger operators

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

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Solutions of mKdV in classes of functions unbounded at infinity

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ASJC Scopus subject areas

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