Model reduction of a higher-order KdV equation for shallow water waves

Tassos Bountis, Ko Van Der Weele, Giorgos Kanellopoulos, Kostis Andriopoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

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 languageEnglish
Title of host publicationCoping with Complexity: Model Reduction and Data Analysis
Pages287-298
Number of pages12
Volume75 LNCSE
DOIs
Publication statusPublished - 2011
Externally publishedYes
EventInternational Research Workshop: Coping with Complexity: Model Reduction and Data Analysis - Ambleside, United Kingdom
Duration: Aug 31 2009Sep 4 2009

Publication series

NameLecture Notes in Computational Science and Engineering
Volume75 LNCSE
ISSN (Print)14397358

Other

OtherInternational Research Workshop: Coping with Complexity: Model Reduction and Data Analysis
CountryUnited Kingdom
CityAmbleside
Period8/31/099/4/09

Fingerprint

Shallow Water Waves
Higher order equation
Model Reduction
KdV Equation
Water waves
Solitons
Solitary Wave Solution
Solitary Waves
Partial differential equation
Generalized KdV Equation
Partial differential equations
Water Waves
Breakdown
Ordinary differential equation
Initial conditions
Ordinary differential equations
Water
Experiment
Standards
Profile

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mathematics
  • Modelling and Simulation
  • Control and Optimization
  • Discrete Mathematics and Combinatorics

Cite this

Bountis, T., Van Der Weele, K., Kanellopoulos, G., & Andriopoulos, K. (2011). Model reduction of a higher-order KdV equation for shallow water waves. In 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.

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 proceedingConference contribution

Bountis, T, Van Der Weele, K, Kanellopoulos, G & Andriopoulos, K 2011, Model reduction of a higher-order KdV equation for shallow water waves. in 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
Bountis T, Van Der Weele K, Kanellopoulos G, Andriopoulos K. Model reduction of a higher-order KdV equation for shallow water waves. In Coping with Complexity: Model Reduction and Data Analysis. Vol. 75 LNCSE. 2011. p. 287-298. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-14941-2_15
Bountis, Tassos ; Van Der Weele, Ko ; Kanellopoulos, Giorgos ; Andriopoulos, Kostis. / Model reduction of a higher-order KdV equation for shallow water waves. Coping with Complexity: Model Reduction and Data Analysis. Vol. 75 LNCSE 2011. pp. 287-298 (Lecture Notes in Computational Science and Engineering).
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