Solitons from the Lagrangian perspective

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Deep-water waves with vorticity: symmetry and rotational behaviour

September 2007, 19(3): 469-481. doi: 10.3934/dcds.2007.19.469

Solitons from the Lagrangian perspective

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

Received March 2007 Revised June 2007 Published July 2007

Abstract
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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.

Keywords: soliton, particle trajectory., solitary wave.

Mathematics Subject Classification: Primary: 35Q51, 76B2.

Citation: Adrian Constantin. Solitons from the Lagrangian perspective. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 469-481. doi: 10.3934/dcds.2007.19.469

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