2 citations · 2 across the 4 of their papers we have counts for
10 papers · 1 filter
Asymptotic expansion of the wobbling kink
O F Oxtoby, I V Barashenkov
The method of multiple scales is used to study the wobbling kink of the equation. The amplitude of the wobbling is shown to decay very slowly, as , and hence the wo…
Stability of the Bloch wall via the Bogomolnyi decomposition in elliptic coordinates
S R Woodford, I V Barashenkov
We consider the one-dimensional anisotropic XY model in the continuum limit. Stability analysis of its Bloch wall solution is hindered by the nondiagonality of the associated linea…
Exceptional discretisations of the sine-Gordon equation
I. V. Barashenkov, T. C. van Heerden
Recently, the method of one-dimensional maps was introduced as a means of generating exceptional discretisations of the -theories, i.e., discrete -models which support ki…
Interactions of Parametrically Driven Dark Solitons. II: Néel-Bloch interactions
I. V. Barashenkov, S. R. Woodford
The interaction between a Bloch and a Néel wall in the parametrically driven nonlinear Schrödinger equation is studied by following the dissociation of their unstable bound state.…
Translationally invariant discrete kinks from one-dimensional maps
I. V. Barashenkov, O. F. Oxtoby, Dmitry E. Pelinovsky
For most discretisations of the theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional disc…
Travelling kinks in discrete phi^4 models
O. F. Oxtoby, D. E. Pelinovsky, I. V. Barashenkov
In recent years, three exceptional discretizations of the phi^4 theory have been discovered [J.M. Speight and R.S. Ward, Nonlinearity 7, 475 (1994); C.M. Bender and A. Tovbis, J. M…