TY - JOUR
T1 - Zooming in
T2 - From spatially extended traveling waves to localized structures: The case of the sine-gordon equation in (1+3) dimensions
AU - Zarmi, Yair
N1 - Publisher Copyright:
© 2017 Yair Zarmi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")-solutions for all N≥1. A nonlinear functional of the solution, which vanishes on a singlefront, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles.
AB - The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")-solutions for all N≥1. A nonlinear functional of the solution, which vanishes on a singlefront, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles.
UR - http://www.scopus.com/inward/record.url?scp=85018511208&partnerID=8YFLogxK
U2 - 10.1371/journal.pone.0175783
DO - 10.1371/journal.pone.0175783
M3 - Article
C2 - 28422999
AN - SCOPUS:85018511208
SN - 1932-6203
VL - 12
JO - PLoS ONE
JF - PLoS ONE
IS - 4
M1 - e0175783
ER -