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Identifiability for Linearized Sine-Gordon Equation

Published online by Cambridge University Press:  28 January 2013

J. Ha  and
S. Gutman
J. Ha
Affiliation:
School of Liberal Arts, Korea University of Technology and Education Cheonan 330-708, South Korea
S. Gutman*
Affiliation:
Department of Mathematics, University of Oklahoma Norman, Oklahoma 73019, USA
*
∗ Corresponding author. E-mail: sgutman@ou.edu
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Abstract

The paper presents theoretical and numerical results on the identifiability, i.e. the unique identification for the one-dimensional sine-Gordon equation. The identifiability for nonlinear sine-Gordon equation remains an open question. In this paper we establish the identifiability for a linearized sine-Gordon problem. Our method consists of a careful analysis of the Laplace and Fourier transforms of the observation of the system, conducted at a single point. Numerical results based on the best fit to data method confirm that the identification is unique for a wide choice of initial approximations for the sought test parameters. Numerical results compare the identification for the nonlinear and the linearized problems.

Keywords

Identificationidentifiabilitysine-Gordon equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 106 - 121
Copyright
© EDP Sciences, 2013

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