Method of lines solution of the Korteweg-de Vries equation

PDF Version Also Available for Download.

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 ... continued below

Physical Description

15 p.

Creation Information

Schiesser, W.E. June 1, 1993.

Context

This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Author

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

Sponsor

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

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.

Notes

INIS; OSTI as DE95011127

Source

  • Other Information: PBD: Jun 1993

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • 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

Collections

This report is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

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

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this report?

When

Dates and time periods associated with this report.

Creation Date

  • June 1, 1993

Added to The UNT Digital Library

  • Aug. 14, 2015, 8:43 a.m.

Description Last Updated

  • April 29, 2016, 5:53 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 3

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

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 November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.