On Integrable Doebner-Goldin Equations

Details On Integrable Doebner-Goldin Equations On Integrable Doebner-Goldin Equations

1995-10-10

arxiv.org/abs/solv-int/9510001v1

J.Phys.A29:2869-2886,1996

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.sty

Scientific paper

10.1088/0305-4470/29/11/021

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.

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