Abstract
We present novel results on a non-integrable generalized KdV equation proposed by Fokas [A.S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional solitary water waves with greater accuracy than the standard KdV equation. The profile of the solitary wave solutions is determined via a reduction of the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). Subsequently, we study the stability of the wave using this profile as initial condition for the PDE. In the case of the standard KdV equation it is well-known that the solitary wave solutions are always stable, irrespective of their height. However, in the case of our higher-order KdV equation we find that the stability of the solutions breaks down beyond a certain critical height, just like solitary waves in real water experiments.
| Original language | English |
|---|---|
| Title of host publication | Coping with Complexity: Model Reduction and Data Analysis |
| Pages | 287-298 |
| Number of pages | 12 |
| Volume | 75 LNCSE |
| DOIs | |
| Publication status | Published - 2011 |
| Externally published | Yes |
| Event | International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis - Ambleside, United Kingdom Duration: Aug 31 2009 → Sep 4 2009 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Volume | 75 LNCSE |
| ISSN (Print) | 14397358 |
Other
| Other | International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis |
|---|---|
| Country | United Kingdom |
| City | Ambleside |
| Period | 8/31/09 → 9/4/09 |
Fingerprint
ASJC Scopus subject areas
- Engineering(all)
- Computational Mathematics
- Modelling and Simulation
- Control and Optimization
- Discrete Mathematics and Combinatorics
Cite this
Model reduction of a higher-order KdV equation for shallow water waves. / Bountis, Tassos; Van Der Weele, Ko; Kanellopoulos, Giorgos; Andriopoulos, Kostis.
Coping with Complexity: Model Reduction and Data Analysis. Vol. 75 LNCSE 2011. p. 287-298 (Lecture Notes in Computational Science and Engineering; Vol. 75 LNCSE).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Model reduction of a higher-order KdV equation for shallow water waves
AU - Bountis, Tassos
AU - Van Der Weele, Ko
AU - Kanellopoulos, Giorgos
AU - Andriopoulos, Kostis
PY - 2011
Y1 - 2011
N2 - We present novel results on a non-integrable generalized KdV equation proposed by Fokas [A.S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional solitary water waves with greater accuracy than the standard KdV equation. The profile of the solitary wave solutions is determined via a reduction of the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). Subsequently, we study the stability of the wave using this profile as initial condition for the PDE. In the case of the standard KdV equation it is well-known that the solitary wave solutions are always stable, irrespective of their height. However, in the case of our higher-order KdV equation we find that the stability of the solutions breaks down beyond a certain critical height, just like solitary waves in real water experiments.
AB - We present novel results on a non-integrable generalized KdV equation proposed by Fokas [A.S. Fokas, Physica D87, 145 (1995)], aiming to describe unidirectional solitary water waves with greater accuracy than the standard KdV equation. The profile of the solitary wave solutions is determined via a reduction of the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). Subsequently, we study the stability of the wave using this profile as initial condition for the PDE. In the case of the standard KdV equation it is well-known that the solitary wave solutions are always stable, irrespective of their height. However, in the case of our higher-order KdV equation we find that the stability of the solutions breaks down beyond a certain critical height, just like solitary waves in real water experiments.
UR - http://www.scopus.com/inward/record.url?scp=78651528385&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78651528385&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-14941-2_15
DO - 10.1007/978-3-642-14941-2_15
M3 - Conference contribution
AN - SCOPUS:78651528385
SN - 9783642149405
VL - 75 LNCSE
T3 - Lecture Notes in Computational Science and Engineering
SP - 287
EP - 298
BT - Coping with Complexity: Model Reduction and Data Analysis
ER -