Collective Properties of Neural Systems and Their Relation to Other Physical Models.

摘要

During the tenure of this contract we have been able to characterize solitons in multidimensions. It is well known that there exist several physically important equations in two dimensions (e.g. KdV, NLS) that support certain stable coherent structures called solitons. The solitons in the last 20 years have played an important role in the understanding of many physical and biological phenomena. Although there exist several equations in three dimensions, which share many features with the soliton equations in two dimensions (e.g. KP, DS), these equations could not so far support soliton solutions. We have recently found coherent structures for such equations; these structures have many novel properties not found in the 1+1 solitons and we have called them DROMIONS. The author and V. Zakharov have shown that in addition to Davey-Stewartson equation, many other physical significant nonlinear equations can support Dromions. (kt)