TY - JOUR
T1 - Compactification of nonlinear patterns and waves
AU - Rosenau, Philip
AU - Kashdan, Eugene
PY - 2008/12/22
Y1 - 2008/12/22
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=58149271057&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.101.264101
DO - 10.1103/PhysRevLett.101.264101
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AN - SCOPUS:58149271057
SN - 0031-9007
VL - 101
JO - Physical Review Letters
JF - Physical Review Letters
IS - 26
M1 - 264101
ER -