TY - JOUR
T1 - Interaction of sine-Gordon kinks with defects
T2 - The two-bounce resonance
AU - Goodman, Roy H.
AU - Haberman, Richard
N1 - Funding Information:
We would like to thank Phil Holmes, Michael Weinstein, Greg Kriegsmann, and Chris Raymond for helpful discussions. RG was supported by NSF DMS-0204881 and by an SBR grant from NJIT.
PY - 2004/8/15
Y1 - 2004/8/15
N2 - A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analytical formulas for the locations of the well known two- and three-bounce resonance windows, as well as several other phenomena seen in numerical simulations.
AB - A model of soliton-defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov theory is used to derive a critical velocity for strong interactions, which is shown to be exponentially small for weak defects. Matched asymptotic expansions for nearly heteroclinic orbits are constructed for the initial value problem, which are then used to derive analytical formulas for the locations of the well known two- and three-bounce resonance windows, as well as several other phenomena seen in numerical simulations.
KW - Sine-Gordon kinks
KW - Singular perturbation theory
KW - Two-bounce resonance
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U2 - 10.1016/j.physd.2004.04.002
DO - 10.1016/j.physd.2004.04.002
M3 - Article
AN - SCOPUS:3342892305
SN - 0167-2789
VL - 195
SP - 303
EP - 323
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -