New models for multi-dimensional stable vortex solitons
Solitons are stable solitary waves.In 1834,Scott Russel first observed such a solitary water wave in a narrow channel near Edinburgh.In 1895,D.Korteweg and G.de Vries had derived the Korteweg-de Vries (KdV) equations for waves on shallow water surfaces.In 1965,N.Zabusky and M.Kruskal had demonstrated the stability of the solitary waves in the Korteweg-de Vries equation using numerical simulations,and coined the term “soliton”.In 1967,Gardner,Greene,Kruskal,and Miura had discovered the mathematical technique of the inverse scattering transform to find analytical solutions to the KdV equation in a systematic manner,and the KdV equation was thus recognized as a paradigmatic integrable partial differential equation.The nonlinear Schr(o)dinger (NLS) equation is another extremely important integrable system,which has a form of i(6)tφ =(-1/2)(6)xxφ + g|φ|2φ.There are plane-wave solutions to this equation,however,the cubic self-focusing nonlinear term (with g < 0) causes modulational instability and creates solitary waves.The NLS equation can model gravity waves on the surface of deep inviscid water and light waves in various optical media,as well as many other physical media.A great many of papers and books about solitons have been published ”1-3”.
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2019-05-06(万方平台首次上网日期,不代表论文的发表时间)
共2页
87-88