Some Exact Solutions of a Nonintegrable Toda-type Equation

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We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

Original languageEnglish
Pages (from-to)1000-1004
Number of pages5
JournalJournal of the Korean Physical Society
Issue number9
StatePublished - 1 May 2018

Bibliographical note

Publisher Copyright:
© 2018, The Korean Physical Society.


  • Chern-Simons theory
  • Toda equation
  • Vortex


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