### 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 |
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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 |
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Volume | 75 LNCSE |

ISSN (Print) | 14397358 |

### Other

Other | International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis |
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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

*Coping with Complexity: Model Reduction and Data Analysis*(Vol. 75 LNCSE, pp. 287-298). (Lecture Notes in Computational Science and Engineering; Vol. 75 LNCSE). https://doi.org/10.1007/978-3-642-14941-2_15

**Model reduction of a higher-order KdV equation for shallow water waves.** / Bountis, Tassos; Van Der Weele, Ko; Kanellopoulos, Giorgos; Andriopoulos, Kostis.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Coping with Complexity: Model Reduction and Data Analysis.*vol. 75 LNCSE, Lecture Notes in Computational Science and Engineering, vol. 75 LNCSE, pp. 287-298, International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis, Ambleside, United Kingdom, 8/31/09. https://doi.org/10.1007/978-3-642-14941-2_15

}

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 -