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

DOI

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

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Beatrice Pelloni
PY  - 2005
DA  - 2005/11/01
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  - 10.2991/jnmp.2005.12.4.6
ID  - Pelloni2005
ER  -