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KdV ’95 pp 361-378 | Cite as

Symbolic Software for Soliton Theory

  • W. Hereman
  • W. Zhuang

Abstract

Four symbolic programs, in Macsyma or Mathematica language, are presented. The first program tests forthe existence of solitons for nonlinear PDEs. It explicitly constructs solitons using Hirota’s bilinear method. In the second program, the Painlevé integrability test for ODEs and PDEs is implemented. The third program provides an algorithm to compute conserved densities for nonlinear evolution equations. The fourth software package aids in the computation of Lie symmetries of systems of differential and difference-differential equations. Several examples illustrate the capabilities of the software.

Key words

soliton theory symbolic programs Hirota method Painlevé test Lie symmetries conserved densities 

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • W. Hereman
    • 1
  • W. Zhuang
    • 1
  1. 1.Department of Mathematical and Computer SciencesColorado School of MinesGoldenUSA

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