STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS

Richard Beals; Peter C. Greiner

doi:10.1142/S0219530509001335

STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS

Richard Beals^*, Peter C. Greiner

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

This survey treats a number of interconnected topics related in one way or another to the famous paper of Mark Kac, "Can one hear the shape of a drum?": wave motion, classical and quantum inverse problems, integrable systems, and the relations between spectra and geometry. We sketch the history and some of the principal developments from the vibrating string to quantum inverse problems, the KdV equation and integrable systems, spectral geometry and the index problem. © World Scientific Publishing Company

Original language	English
Pages (from-to)	131-183
Number of pages	53
Journal	Analysis and Applications
Volume	7
Issue number	2
DOIs	https://doi.org/10.1142/S0219530509001335
Publication status	Published - Apr 2009
Externally published	Yes

Research Keywords

Inverse problems
differential operators
solitons
spectral asymptotics
index theorems
wave motion
KORTEWEG-DE-VRIES
DIFFERENTIAL-EQUATIONS
HEAT-EQUATION
CAMASSA-HOLM
SCATTERING
OPERATORS
MANIFOLDS
SOLITONS
EIGENVALUES
SYMMETRIES

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10.1142/S0219530509001335

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title = "STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS",

abstract = "This survey treats a number of interconnected topics related in one way or another to the famous paper of Mark Kac, {"}Can one hear the shape of a drum?{"}: wave motion, classical and quantum inverse problems, integrable systems, and the relations between spectra and geometry. We sketch the history and some of the principal developments from the vibrating string to quantum inverse problems, the KdV equation and integrable systems, spectral geometry and the index problem. {\textcopyright} World Scientific Publishing Company",

keywords = "Inverse problems, differential operators, solitons, spectral asymptotics, index theorems, wave motion, KORTEWEG-DE-VRIES, DIFFERENTIAL-EQUATIONS, HEAT-EQUATION, CAMASSA-HOLM, SCATTERING, OPERATORS, MANIFOLDS, SOLITONS, EIGENVALUES, SYMMETRIES",

author = "Richard Beals and Greiner, {Peter C.}",

year = "2009",

month = apr,

doi = "10.1142/S0219530509001335",

language = "English",

volume = "7",

pages = "131--183",

journal = "Analysis and Applications",

issn = "0219-5305",

publisher = "World Scientific",

number = "2",

}

TY - JOUR

T1 - STRINGS, WAVES, DRUMS

T2 - SPECTRA AND INVERSE PROBLEMS

AU - Beals, Richard

AU - Greiner, Peter C.

PY - 2009/4

Y1 - 2009/4

N2 - This survey treats a number of interconnected topics related in one way or another to the famous paper of Mark Kac, "Can one hear the shape of a drum?": wave motion, classical and quantum inverse problems, integrable systems, and the relations between spectra and geometry. We sketch the history and some of the principal developments from the vibrating string to quantum inverse problems, the KdV equation and integrable systems, spectral geometry and the index problem. © World Scientific Publishing Company

AB - This survey treats a number of interconnected topics related in one way or another to the famous paper of Mark Kac, "Can one hear the shape of a drum?": wave motion, classical and quantum inverse problems, integrable systems, and the relations between spectra and geometry. We sketch the history and some of the principal developments from the vibrating string to quantum inverse problems, the KdV equation and integrable systems, spectral geometry and the index problem. © World Scientific Publishing Company

KW - Inverse problems

KW - differential operators

KW - solitons

KW - spectral asymptotics

KW - index theorems

KW - wave motion

KW - KORTEWEG-DE-VRIES

KW - DIFFERENTIAL-EQUATIONS

KW - HEAT-EQUATION

KW - CAMASSA-HOLM

KW - SCATTERING

KW - OPERATORS

KW - MANIFOLDS

KW - SOLITONS

KW - EIGENVALUES

KW - SYMMETRIES

U2 - 10.1142/S0219530509001335

DO - 10.1142/S0219530509001335

M3 - RGC 21 - Publication in refereed journal

SN - 0219-5305

VL - 7

SP - 131

EP - 183

JO - Analysis and Applications

JF - Analysis and Applications

IS - 2

ER -

STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS

Abstract

Research Keywords

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