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Dark Solitons for the Defocusing Cubic Nonlinear Schr?dinger Equation with the Spatially Periodic Potential and Nonlinearity
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作者 闫振亚 闫方驰 《Communications in Theoretical Physics》 SCIE CAS CSCD 2015年第9期309-319,共11页
We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower sol... We study the existence of dark solitons of the defocusing cubic nonlinear Schr¨odinger(NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincar′e map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity. 展开更多
关键词 DEFOCUSING CUBIC NLS EQUATION the theory of UPPER
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