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Method of lines solution of the Korteweg-de Vries equation

Technical Report ·
DOI:https://doi.org/10.2172/64337· OSTI ID:64337
 [1]
  1. Superconducting Super Collider Lab., Dallas, TX (United States)
The Korteweg-de Vries equation (KdVE) is a classical nonlinear partial differential equation (PDE) originally formulated to model shallow water flow. In addition to the applications in hydrodynamics, the KdVE has been studied to elucidate interesting mathematical properties. In particular, the KDVE balances front sharpening and dispersion to produce solitons, i.e., traveling waves that do not change shape or speed. In this paper, we compute a solution of the KdVE by the method of lines (MOL) and compare this numerical solution with the analytical solution of the KdVE. In a second numerical solution, we demonstrate how solitons of the KdVE traveling at different velocities can merge and emerge. The numerical procedure described in the paper demonstrates the ease with which the MOL can be applied to the solution of PDEs using established numerical approximations implemented in library routines.
Research Organization:
Superconducting Super Collider Lab., Dallas, TX (United States)
Sponsoring Organization:
USDOE, Washington, DC (United States)
DOE Contract Number:
AC35-89ER40486
OSTI ID:
64337
Report Number(s):
SSCL-Preprint--443; ON: DE95011127
Country of Publication:
United States
Language:
English

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