Stable two-dimensional soliton supported by a local nonlinearity

Er’el Granot, Boris A. Malomed

Research output: Contribution to journalArticlepeer-review


We show that an attractive nonlinear potential in the form of a modified Azbel two-dimensional (2D) δ function (that, unlike the traditional 2D δ function, gives rise to a well-defined bound state in quantum mechanics) supports a 2D localized state (“soliton”), that may be stable according to the Vakhitov-Kolokolov (VK) criterion, provided that the soliton’s amplitude is not too small. A direct, although not general, dynamical stability consideration yields results in compliance with the VK criterion.

Original languageEnglish
Pages (from-to)2185-2187
Number of pages3
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - 2000


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