Evolution of two-dimensional lump nanosolitons for the Zakharov-Kuznetsov and electromigration equations

M C Jorge, G Cruz-Pacheco, L Mier-y-Teran-Romero, N F Smyth

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lumplike initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation. (C) 2005 American Institute of Physics.

Original languageEnglish
Article number037104
Pages (from-to)-
Number of pages13
JournalChaos: An Interdisciplinary Journal of Nonlinear Science
Volume15
Issue number3
DOIs
Publication statusPublished - Sept 2005

Keywords / Materials (for Non-textual outputs)

  • SOLITON STABILITY
  • PLASMAS

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