Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model

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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.
Original languageEnglish
Pages (from-to)917-934
Number of pages18
JournalJournal of Nonlinear Science
Issue number6
Early online date18 May 2012
Publication statusPublished - Dec 2012


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