The Klein-Gordon Equation on the Half Line: a Riemann-Hilbert Approach

DOI

10.2991/jnmp.2008.15.s3.32How to use a DOI?

Abstract

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Copyright

© 2008, 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
AU  - Dimitrios A. Pinotsis
PY  - 2008
DA  - 2008/10/01
TI  - The Klein-Gordon Equation on the Half Line: a Riemann-Hilbert Approach
JO  - Journal of Nonlinear Mathematical Physics
SP  - 334
EP  - 344
VL  - 15
IS  - supplement 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.s3.32
DO  - 10.2991/jnmp.2008.15.s3.32
ID  - Pelloni2008
ER  -