@article{38966,
  keywords = {topological solitons},
  author = {P. G. Kevrekidis and F. L. Williams and A. R. Bishop and I. G. Kevrekidis and B. A. Malomed},
  title = {Coupling fields and underlying space curvature: An augmented Lagrangian approach},
  abstract = { <p>We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space{\textquoteright}s metric tensor to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent (which gives rise to an ordinary differential equation for its temporal evolution), and the other with spatiotemporal dependence (wherein the metric{\textquoteright}s evolution is governed by a partial differential equation). Numerical results are reported for the (1 + 1)-dimensional model with a nonlinearity of the sine-Gordon type.</p> },
  year = {2003},
  journal = {Physical Review E},
  volume = {67},
  pages = {047602},
  month = {04/2003},
  isbn = {1539-3755},
  language = {English},
}