TY - JOUR
T1 - On quintic equations with a linear window
AU - Rosenau, Philip
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2016/1/8
Y1 - 2016/1/8
N2 - We study a quintic dispersive equation ut=[au2+b(uuxx+βux2)+c(uu4x+2q1uxu3x+q2uxx2)]x and show that if β=q1=-q2, it may be cast into vt=[vLωu]x, where v=uω, ω=2β+1 and Lω is a fourth order linear operator. This enables to construct traveling patterns via superposition of solutions. A plethora of bell-shaped, multi-humped and asymmetric compacton, is found. Their interaction ranges from being almost elastic to a noisy one, including fusion of bell-shaped compactons and anti-compactons into robust asymmetric structures. A stationary, zero-mass, doublet-like compacton is found to be an attractor of topologically similar, zero-mass, excitations.
AB - We study a quintic dispersive equation ut=[au2+b(uuxx+βux2)+c(uu4x+2q1uxu3x+q2uxx2)]x and show that if β=q1=-q2, it may be cast into vt=[vLωu]x, where v=uω, ω=2β+1 and Lω is a fourth order linear operator. This enables to construct traveling patterns via superposition of solutions. A plethora of bell-shaped, multi-humped and asymmetric compacton, is found. Their interaction ranges from being almost elastic to a noisy one, including fusion of bell-shaped compactons and anti-compactons into robust asymmetric structures. A stationary, zero-mass, doublet-like compacton is found to be an attractor of topologically similar, zero-mass, excitations.
KW - Compactons
KW - Exact linearization,
KW - Interaction
KW - Quintic dispersive waves
KW - Solitons
KW - Volterra-Lotke system
UR - http://www.scopus.com/inward/record.url?scp=84946780809&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2015.09.045
DO - 10.1016/j.physleta.2015.09.045
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AN - SCOPUS:84946780809
SN - 0375-9601
VL - 380
SP - 135
EP - 141
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-2
ER -