Solitons from the Lagrangian perspective

Adrian Constantin

doi:10.3934/dcds.2007.19.469

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2007, Volume 19, Issue 3: 469-481. Doi: 10.3934/dcds.2007.19.469

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Solitons from the Lagrangian perspective

Adrian Constantin^1,

1.
School of Mathematics, Trinity College Dublin, Dublin 2

Received: March 2007

Revised: June 2007

Published: September 2007

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Abstract

The soliton solution of the Korteweg-de Vries equation provides a good approximation to the shape of a solitary wave solution to the governing equations for water waves. However, the corresponding velocity field below the soliton is not an accurate approximation. We propose an approach that provides us with a better approximation. By describing the particle paths below the free surface, we show that the qualitative features of the entire flow in a solitary water wave is captured by our approximation of the velocity field.

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Mathematics Subject Classification: Primary: 35Q51, 76B25.

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