On Integrable Doebner-Goldin Equations
solv-int
2008-11-26 v1 高能物理 - 理论
可精确求解与可积系统
量子物理
摘要
We suggest a method for integrating sub-families of a family of nonlinear {\sc Schr\"odinger} equations proposed by {\sc H.-D.~Doebner} and {\sc G.A.~Goldin} in the 1+1 dimensional case which have exceptional {\sc Lie} symmetries. Since the method of integration involves non-local transformations of dependent and independent variables, general solutions obtained include implicitly determined functions. By properly specifying one of the arbitrary functions contained in these solutions, we obtain broad classes of explicit square integrable solutions. The physical significance and some analytical properties of the solutions obtained are briefly discussed.
引用
@article{arxiv.solv-int/9510001,
title = {On Integrable Doebner-Goldin Equations},
author = {P. Nattermann and R. Zhdanov},
journal= {arXiv preprint arXiv:solv-int/9510001},
year = {2008}
}
备注
23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.sty