Designable Integrability of the Variable Coefficient Nonlinear Schrodinger Equations
Designable Integrability of the Variable Coefficient Nonlinear Schrodinger Equations
复制标题
变系数非线性薛定谔方程的可设计可积性
DOI：
10.1111/j.1467-9590.2010.00495.x
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发表时间：
2011-01-01
影响因子：
2.7
通讯作者：
Li, Y.
中科院分区：
文献类型：
--
作者：
He, J.;Li, Y.
通过构造一个将变系数非线性薛定谔方程映射到一般非线性薛定谔方程的显式变换，引入了变系数非线性薛定谔方程的可设计可积性。基于DI的VCNLSE的一个新特点是它的系数可以通过变换进行人工设计和解析。本文给出了非自治nlse与nlse之间的一个特殊例子。此外，还设计了玻色-爱因斯坦凝聚和非线性光学系统中两种重要的光学超晶格势（或周期势）和多阱势。解析公式和精确公式表明了vcnlse孤子的两个有趣特征。具体来说，它的轮廓是可变的，随着时间t的变化，它的轨迹不是一条直线。
The designable integrability (DI) [51] of the variable coefficient nonlinear Schrodinger equations (VCNLSEs) is first introduced by construction of an explicit transformation, which maps VCNLSE to the usual nonlinear Schrodinger equations (NLSEs). One novel feature of VCNLSE with DI is that its coefficients can be designed artificially and analytically by using transformation. A special example between nonautonomous NLSEs and NLSEs is given here. Further, the optical super-lattice potentials (or periodic potentials) and multiwell potentials are designed, which are two kinds of important potential in Bose-Einstein condensation and nonlinear optical systems. There are two interesting features of the soliton of the VCNLSEs indicated by the analytic and exact formula. Specifically, its profile is variable and its trajectory is not a straight line when it evolves with time t.