Compact patterns in a class of sublinear Gardner equations

Philip Rosenau, Alexander Oron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study a class of sublinear Gardner equations ut+−uα±mumx+uxxx=0, where 0<α<1<m, which exhibit two distinguished features; their solitary waves have a finite span, i.e., are compactons and, depending on their amplitude, may propagate either to the right or to the left, and thus undergo both chase and head-on interactions or, switch direction upon collision. All in all, their morphology, is vastly richer than encountered in the unidirectional KdV-like equations. The multi-dimensional extension ut+−uα±mumx+(∇2u)x=0, reveals an even richer landscape; each admissible velocity supports an entire spectrum of multi-nodal compactons.

Original languageEnglish
Article number106384
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Jul 2022


  • Compactons
  • Flatons
  • Sublinear Gardner equation


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