Abstract
We extend the dispersion-velocity particle method that we recently introduced to advection models in which the velocity does not depend linearly on the solution or its derivatives. An example is the Korteweg de Vries (KdV) equation for which we derive a particle method and demonstrate numerically how it captures soliton–soliton interactions.
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Chertock, A., Levy, D. A Particle Method for the KdV Equation. Journal of Scientific Computing 17, 491–499 (2002). https://doi.org/10.1023/A:1015106210404
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DOI: https://doi.org/10.1023/A:1015106210404