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 - 2011/1/1
Y1 - 2011/1/1
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.
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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
T3 - Lecture Notes in Computational Science and Engineering
SP - 287
EP - 298
BT - Coping with Complexity
T2 - International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis
Y2 - 31 August 2009 through 4 September 2009
ER -