1995/10/10 by P. Nattermann, Renat Zhdanov, R. Zhdanov · 2 citations
Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #nlin.SI #quant-ph #solv-int
paper · pdf · doi:10.1088/0305-4470/29/11/021
published as J.Phys.A29:2869-2886,1996 · 23 pages, revtex, 1 figure, uses epsfig.sty and amssymb.sty
arxiv created 1995/10/10 · openalex publication_date 1996/06/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We integrate sub-families of a family of nonlinear Schrödinger equations proposed by Doebner and Goldin in the (1 + 1)-dimensional case which have exceptional 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.