On solitary patterns in Lotka-Volterra chains

Alon Zilburg, Philip Rosenau

Research output: Contribution to journalArticlepeer-review


We present and study a class of Lotka-Volterra chains with symmetric 2N-neighbors interactions. To identify the types of solitary waves which may propagate along the chain, we study their quasi-continuum approximations which, depending on the coupling between neighbors, reduce into a large variety of partial differential equations. Notable among the emerging equations is a bi-cubic equation ut = [bu2 + 2κuu + (uxx)2]x which we study in some detail. It begets remarkably stable topological and non-topological solitary compactons that interact almost elastically. They are used to identify discretons, their solitary discrete antecedents on the lattice, which decay at a doubly exponential rate. Many of the discrete modes are robust while others either decompose or evolve into breathers.

Original languageEnglish
Article number095101
JournalJournal of Physics A: Mathematical and Theoretical
Issue number9
StatePublished - 25 Jan 2016


  • bi-cubic pde
  • breathers
  • compactons
  • extended Lotka-Volterra chains
  • quasi-continuum
  • solitons


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