TY - JOUR
T1 - Variational approximations to homoclinic snaking
AU - Susanto, H.
AU - Matthews, P. C.
PY - 2011/3/31
Y1 - 2011/3/31
N2 - We investigate the snaking of localized patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, which are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric "ladder" states, and also predict the stability of the localized states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.
AB - We investigate the snaking of localized patterns, seen in numerous physical applications, using a variational approximation. This method naturally introduces the exponentially small terms responsible for the snaking structure, which are not accessible via standard multiple-scales asymptotic techniques. We obtain the symmetric snaking solutions and the asymmetric "ladder" states, and also predict the stability of the localized states. The resulting approximate formulas for the width of the snaking region show good agreement with numerical results.
UR - http://www.scopus.com/inward/record.url?scp=79961113083&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.83.035201
DO - 10.1103/PhysRevE.83.035201
M3 - Article
AN - SCOPUS:79961113083
SN - 1539-3755
VL - 83
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 035201
ER -