Journal of Nonlinear Mathematical Physics

Volume 22, Issue 1, December 2014, Pages 102 - 116

On a spectral analysis of scattering data for the Camassa-Holm equation

Authors
Chueh-Hsin Chang, Tony Wen-Hann Sheu*
Center of Advanced Study in Theoretical Sciences, National Taiwan University, Taipei, 10617, Taiwan.changjuexin@tims.ntu.edu.tw
Center of Advanced Study in Theoretical Sciences Department of Engineering Science and Ocean Engineering Institute of Applied Mathematical Science National Taiwan University, Taipei, 10617, Taiwan,twhsheu@ntu.edu.tw
* Corresponding author
Corresponding Author
Tony Wen-Hann Sheu
Received 30 August 2014, Accepted 6 October 2014, Available Online 6 January 2021.
DOI
10.1080/14029251.2015.996443How to use a DOI?
Keywords
direct and inverse scattering; Camassa-Holm equation; isospectral problem
Abstract

Physical details of the Camassa–Holm (CH) equation that are difficult to obtain in space-time simulation can be explored by solving the Lax pair equations within the direct and inverse scattering analysis context. In this spectral analysis of the completely integrable CH equation we focus solely on the direct scattering analysis of the initial condition defined in the physical space coordinate through the time-independent Lax equation. Both of the continuous and discrete spectrum cases for the initial condition under current investigation are analytically derived. The scattering data derived from the direct scattering transform for non-reflectionless case are also discussed in detail in spectral domain from the physical viewpoint.

Copyright
© 2015 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
22 - 1
Pages
102 - 116
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2015.996443How to use a DOI?
Copyright
© 2015 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Chueh-Hsin Chang
AU  - Tony Wen-Hann Sheu
PY  - 2021
DA  - 2021/01/06
TI  - On a spectral analysis of scattering data for the Camassa-Holm equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 102
EP  - 116
VL  - 22
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.996443
DO  - 10.1080/14029251.2015.996443
ID  - Chang2021
ER  -