A Lie group investigation of exact weakly nonlinear quasi-planar sound waves

C. Wafo Soh, Ebrahim Momoniat

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The Lie point symmetries of the (1+2)D Zabolotskaya-Khokholov (ZK) equation for a gas with nonzero viscosity at rest are calculated. They form an infinite-dimensional Lie algebra which can be written as the direct sum of a 2D Lie algebra and an infinite-dimensional Lie algebra. The symmetry structure of the ZK equation is used to construct its physically relevant solutions from those of the (1 + 1)D Burgers equation. In particular, travelling wave solutions (one-solitons) as well as the multi-soliton solutions of the ZK equation are obtained. Also, we obtain the N-waves, the periodic waves and the solution to some Cauchy problems for the ZK equation. We emphasize that our method can be utilized to generate a wider class of solutions of the ZK equation.

Original languageEnglish
Pages (from-to)219-232
Number of pages14
JournalIMA Journal of Applied Mathematics
Issue number3
Publication statusPublished - Jun 2004
Externally publishedYes


  • Lie group method
  • Travelling wave solutions
  • Zabolotskaya-Khokholov (ZK) equation

ASJC Scopus subject areas

  • Applied Mathematics


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