Properties of the Magma and Modified Magma Equations

Daisuke Takahashi, Junkichi Satsuma, Jeffrey R. Sachs

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


Solutions of the “magma equation”, ft=[fn{(f-mft)x-1}]x, are investigated for compact support initial conditions. It is shown analytically that traveling wave solutions with compact support do not exist for this equation. Numerical integration demonstrates that although initial conditions with compact support produce solitary waves, these solitary waves do not interact like solitons. Moreover, a relationship between the magma equation and the KdV equation is established, and this relationship is used to explain previously observed soliton-like behavior. Both equations are shown to be related to the modified magma equation, FT+[F3(3FXX+1)]x=0, which is proven to have N-soliton solutions with compact support and an infinite number of conserved densities.

Original languageEnglish
Pages (from-to)1941-1953
Number of pages13
Journaljournal of the physical society of japan
Issue number6
Publication statusPublished - 1990
Externally publishedYes


  • KdV equation
  • compact support solution
  • integrable
  • magma equation
  • soliton

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Properties of the Magma and Modified Magma Equations'. Together they form a unique fingerprint.

Cite this