Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 19, Issue 3, Pages 469-481Publisher
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/dcds.2007.19.469
Keywords
solitary wave; soliton; particle trajectory
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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.
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