TY - JOUR
T1 - Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model
AU - Schwetlick, Hartmut
AU - Sutton, Daniel C
AU - Zimmer, Johannes
PY - 2012/12
Y1 - 2012/12
N2 - The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two stable phases. We demonstrate that there is no travelling wave joining bounded strains in the different wells of this potential for a range of wave speeds significantly lower than the speed of sound. We achieve this using a profile-corrector method previously used to show existence of travelling waves for the same model at higher subsonic velocities.
AB - The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two stable phases. We demonstrate that there is no travelling wave joining bounded strains in the different wells of this potential for a range of wave speeds significantly lower than the speed of sound. We achieve this using a profile-corrector method previously used to show existence of travelling waves for the same model at higher subsonic velocities.
UR - http://www.scopus.com/inward/record.url?scp=84861068998&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s00332-012-9131-8
U2 - 10.1007/s00332-012-9131-8
DO - 10.1007/s00332-012-9131-8
M3 - Article
SN - 0938-8974
VL - 22
SP - 917
EP - 934
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
IS - 6
ER -