Compactification of nonlinear patterns and waves

Philip Rosenau*, Eugene Kashdan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -utt+[Φ′(ux)]x=P′(u) equation, where Φ′(σ)=σ+βσ3 and endowed with a subquadratic site potential P(u)∼|1-u2|α+1, 0≤α<1, and the Schrödinger iZt+/2Z=G(|Z|)Z equation in a plane with G(A)=γA- δ-σA2, 0<δ≤1.

Original languageEnglish
Article number264101
JournalPhysical Review Letters
Issue number26
StatePublished - 22 Dec 2008


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