Journal of Nonlinear Mathematical Physics

Volume 19, Issue Supplement 1, November 2012, Pages 116 - 136

Solitary Waves in Open Channels with Abrupt Turns and Branching Points

Authors
André Nachbin*, Vanessa da Silva Simões
Instituto Nacional de Matemática Pura e Aplicada, Est. D. Castorina, 110, Rio de Janeiro, RJ, 22460-320, Brazil
Corresponding Author
André Nachbin
Received 4 April 2012, Accepted 30 May 2012, Available Online 28 November 2012.
DOI
https://doi.org/10.1142/S1402925112400116How to use a DOI?
Keywords
Water waves, solitary waves, tsunami in channels
Abstract

The dynamics of solitary waves is studied in intricate domains such as open channels with sharp-bends and branching points. Of particular interest, the wave characteristics at sharp-bends is rationalized by using the Jacobian of the Schwarz–Christoffel transformation. It is observed that it acts in a similar fashion as a topography in other wave models previously studied. Previous numerical studies are revisited. A new very efficient algorithm is described, which computationally solves the problem in much more general channel configurations than presented in the literature. Also the conformal mapping naturally leads to a new strategy regarding the geometrical singularity at the sharp-bends. Finally preliminary results illustrate the use of the mapping's Jacobian at a channel's branching point. A future goal of this study regards deducing accurate reduced (one-dimensional) models for the reflection and transmission of solitary waves on graphs/networks.

Copyright
© 2012 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
19 - Supplement 1
Pages
116 - 136
Publication Date
2012/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925112400116How to use a DOI?
Copyright
© 2012 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  - André Nachbin
AU  - Vanessa da Silva Simões
PY  - 2012
DA  - 2012/11
TI  - Solitary Waves in Open Channels with Abrupt Turns and Branching Points
JO  - Journal of Nonlinear Mathematical Physics
SP  - 116
EP  - 136
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400116
DO  - https://doi.org/10.1142/S1402925112400116
ID  - Nachbin2012
ER  -