dorsal/arxiv
View SchemaOn Integrable Doebner-Goldin Equations
| Authors | P. Nattermann, R. Zhdanov |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9510001 |
| URL | https://arxiv.org/abs/solv-int/9510001 |
| DOI | 10.1088/0305-4470/29/11/021 |
| Journal | J.Phys.A29:2869-2886,1996 |
Abstract
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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"abstract": "We suggest a method for integrating sub-families of a family of nonlinear\n{\\sc Schr\\\"odinger} equations proposed by {\\sc H.-D.~Doebner} and {\\sc\nG.A.~Goldin} in the 1+1 dimensional case which have exceptional {\\sc Lie}\nsymmetries. Since the method of integration involves non-local transformations\nof dependent and independent variables, general solutions obtained include\nimplicitly determined functions. By properly specifying one of the arbitrary\nfunctions contained in these solutions, we obtain broad classes of explicit\nsquare integrable solutions. The physical significance and some analytical\nproperties of the solutions obtained are briefly discussed.",
"arxiv_id": "solv-int/9510001",
"authors": [
"P. Nattermann",
"R. Zhdanov"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI",
"quant-ph"
],
"doi": "10.1088/0305-4470/29/11/021",
"journal_ref": "J.Phys.A29:2869-2886,1996",
"title": "On Integrable Doebner-Goldin Equations",
"url": "https://arxiv.org/abs/solv-int/9510001"
},
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