# American Institute of Mathematical Sciences

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

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.
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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