单模光纤中光孤立子传播的长距离行为(英文)

Long-Distance Behavior of Optical Solitons Propagation in a Monomode Fiber

研究描述单模光纤中光孤立子传播的具光纤损耗项的三阶非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程，首先证明了整体解的存在唯一性结果，然后证明其长距离行为由紧的整体吸引子刻画，并给出了吸引子的Ｈａｕｓｄｏｒｆｆ维数和分形维数的上界估计，最后研究了吸引子的正则性．

We study a third order nonlinear Schrodinger equation with fiber loss term which derives from the propagation of optical soliton in a monomode fiber. We first prove the existence and uniqueness of the global solution, then we show that for some well chosen.coefficients the long-distance behavior of the system is described by a global attractor and that the attractor has finite fractal and Hausdorff dimensions. In addition,we study the regularity of the attractor.