Waves in strongly nonlinear Gardner-like equations on a lattice

Philip Rosenau, Arkady Pikovsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce and study a family of lattice equations which may be viewed either as a strongly nonlinear discrete extension of the Gardner equation, or a non-convex variant of the Lotka-Volterra chain. Their deceptively simple form supports a very rich family of complex solitary patterns. Some of these patterns are also found in the quasi-continuum rendition, but the more intriguing ones, like interlaced pairs of solitary waves, or waves which may reverse their direction either spontaneously or due a collision, are an intrinsic feature of the discrete realm.

Original languageEnglish
Pages (from-to)5872-5896
Number of pages25
Issue number8
StatePublished - Aug 2021


  • Compacton
  • Gardner equation
  • Nonlinear lattice
  • Solitary wave


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