On galilean invariant and energy preserving bbm-type equations
Cheviakov A. Dutykh D. Assylbekuly A.
May 2021MDPI AG
Symmetry
2021#13Issue 5
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.
BENJAMIN–BONA–MAHONY equation , Conservation laws , Nonlinear dispersive waves , Symmetries
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Department of Mathematics and Statistics, University of Saskatchewan, Room 227 McLean Hall, 106 Wiggins Road, Saskatoon, S7N 5E6, SK, Canada
Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAMA, Chambéry, 73000, France
Department of Computational Sciences and Statistics, Al-Farabi Kazakh National University, av. al-Farabi 71, Almaty, 050040, Kazakhstan
Department of Mathematics and Statistics
Univ. Grenoble Alpes
Department of Computational Sciences and Statistics
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