On galilean invariant and energy preserving bbm-type equations

Alexei Cheviakov, Denys Dutykh, Aidar Assylbekuly

Research output: Contribution to journalArticlepeer-review


We investigate a family of higher-order BENJAMIN–BONA–MAHONY-type equations, which appeared in the course of study towards finding a GALILEI-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated CAMASSA–HOLM equation, which confirms its integrability.

Original languageBritish English
Article number878
Issue number5
StatePublished - May 2021


  • Conservation laws
  • Nonlinear dispersive waves
  • Symmetries


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