Method of lines solution of the Korteweg-de Vries equation

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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 ... continued below

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15 p.

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Schiesser, W.E. June 1, 1993.

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  • Schiesser, W.E. Superconducting Super Collider Lab., Dallas, TX (United States)

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Description

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.

Physical Description

15 p.

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INIS; OSTI as DE95011127

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  • Other Information: PBD: Jun 1993

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  • Other: DE95011127
  • Report No.: SSCL-Preprint--443
  • Grant Number: AC35-89ER40486
  • DOI: 10.2172/64337 | External Link
  • Office of Scientific & Technical Information Report Number: 64337
  • Archival Resource Key: ark:/67531/metadc698169

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • June 1, 1993

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  • Aug. 14, 2015, 8:43 a.m.

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  • April 29, 2016, 5:53 p.m.

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Schiesser, W.E. Method of lines solution of the Korteweg-de Vries equation, report, June 1, 1993; Dallas, Texas. (digital.library.unt.edu/ark:/67531/metadc698169/: accessed September 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.