Journal of Nonlinear Mathematical Physics

Volume 12, Issue 4, November 2005, Pages 518 - 529

The Asymptotic Behavior of the Solution of Boundary Value Problems for the sine-Gordon Equation on a Finite Interval

Authors
Beatrice PELLONI
Corresponding Author
Beatrice PELLONI
Received 14 December 2004, Accepted 31 January 2005, Available Online 1 November 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.4.6How to use a DOI?
Abstract
In this article we use thve Fokas transform method to analyze boundary value prolems for the sine-Gordon equation posed on a finite interval. The representation of the solution of this problem has already been derived using this transform method. We interchange the role of the independent variables to obtain an equivalent reprsentation which can be used to study the asymptotic behavior for large times. We use this analysis to prove that the solution corresponding to constant boundary data is dominated for large times by the underlying similarity solution. Dedicated to Francesco Calogero in occasion of his 70th birthday
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 4
Pages
518 - 529
Publication Date
2005/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.4.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Beatrice PELLONI
PY  - 2005
DA  - 2005/11
TI  - The Asymptotic Behavior of the Solution of Boundary Value Problems for the sine-Gordon Equation on a Finite Interval
JO  - Journal of Nonlinear Mathematical Physics
SP  - 518
EP  - 529
VL  - 12
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.4.6
DO  - https://doi.org/10.2991/jnmp.2005.12.4.6
ID  - PELLONI2005
ER  -