Institute for Advanced Study

MATHEMATICS SEMINAR

Multidimensional Solitons

Abstract:

It is commonly known that the interplay of  linear andnonlinear effects  gives rise to solitons, i.e., self-trapped localizedstructures, in a wide range of physical  settings, including optics,Bose-Einstein condensates (BECs), hydrodynamics, plasmas, condensed-matterphysics, etc. Nowadays, solitons are considered as an interdisciplinary classof modes, which feature diverse internal structures. While most experimentalrealizations and theoretical models of solitons have been elaborated inone-dimensional (1D) settings,  a challenging issue is  prediction ofstable solitons in 2D and 3D media. In particular, multidimensional  solitonsmay carry an intrinsic topological structure in the form of vorticity. In  additionto the "simple" vortex solitons, fascinating objects featuringcomplex  structures, such as hopfions, i.e., vortex rings with internaltwist, have been predicted too.  A fundamental problem is propensity ofmultidimensional solitons to being unstable (naturally, solitons with a moresophisticated structure, such as  vortex solitons, are more vulnerable toinstabilities). Recently, novel perspectives for the creation of stable 2D and3D solitons were brought to the attention of researchers in optics and BEC. Thepresent talk aims to provide an overview of the main results and ongoingdevelopments in this vast field. An essential conclusion is the benefit offeredby the exchange of concepts between different areas, such as optics, BEC, and hydrodynamics.
A new review article on the subject: Y. Kartashov, G.Astrakharchik, B. Malomed, and L. Torner, Frontiers in multidimensionalself-trapping of nonlinear fields and matter,

Invited Speaker:  Prof. BorisMalomed

Dept. of Physical Electronics, Tel AvivUniversity

Date: Sept. 3, 2019 (Tuesday)

Time: 3:30-4:30 pm

Venue:Room L3-316, Science and technology building(理工楼), SZU

All are welcome