| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 2, 2018
Shock Waves, Discontinuities and Singularities in Natural Phenomena
|
|
|---|---|---|
| Article Number | 16 | |
| Number of page(s) | 12 | |
| DOI | https://doi.org/10.1051/mmnp/2018026 | |
| Published online | 03 May 2018 | |
Periodic traveling-wave solutions to the Whitham equation
133 Fairway Place,
Sequim,
WA
98382 USA
* Corresponding author: kendall.casey57@yahoo.com
Received:
10
October
2017
Accepted:
11
January
2017
We investigate periodic traveling-wave solutions to the Whitham equation. It is shown that for solutions of this type, the Whitham equation can be expressed as a nonlinear integral equation of Hammerstein form. Solutions to this integral equation are then obtained by iteration. Representative numerical results are presented to illustrate the waveshapes and the nonlinear dispersion characteristics of the solutions thus obtained.
Mathematics Subject Classification: 35Q53 / 45G10 / 47H30
Key words: Whitham equation / traveling waves / Hammerstein integral equation
© EDP Sciences, 2018
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