Journal of Nonlinear Mathematical Physics

Volume 19, Issue Supplement 1, November 2012, Pages 104 - 115

Solitary Traveling Water Waves of Moderate Amplitude

Authors
Anna Geyer
Faculty of Mathematics, University of Vienna, Nordbergstrasse 14, 1090 Vienna, Austria,anna.geyer@univie.ac.at
Received 25 March 2012, Accepted 20 April 2012, Available Online 28 November 2012.
DOI
10.1142/S1402925112400104How to use a DOI?
Keywords
Solitary waves; moderate amplitude; homoclinic orbit
Abstract

We prove the existence of solitary traveling wave solutions for an equation describing the evolution of the free surface for waves of moderate amplitude in the shallow water regime. This nonlinear third-order partial differential equation arises as an approximation of the Euler equations, modeling the unidirectional propagation of surface water waves. We give a description of the solitary wave profiles by performing a phase plane analysis and study some qualitative features of the solutions.

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
104 - 115
Publication Date
2012/11/28
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925112400104How 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  - Anna Geyer
PY  - 2012
DA  - 2012/11/28
TI  - Solitary Traveling Water Waves of Moderate Amplitude
JO  - Journal of Nonlinear Mathematical Physics
SP  - 104
EP  - 115
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400104
DO  - 10.1142/S1402925112400104
ID  - Geyer2012
ER  -