Improved models of dense anharmonic lattices

P. Rosenau, A. Zilburg

Research output: Contribution to journalArticlepeer-review


We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE.

Original languageEnglish
Pages (from-to)87-93
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number2
StatePublished - 15 Jan 2017


  • Anharmonic lattices
  • Compactons
  • Improved PDE description
  • Quartic and Hertz potentials


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