dorsal/arxiv
View SchemaFinite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation
| Authors | E. C. Caparelli, V. V. Dodonov, S. S. Mizrahi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9811016 |
| URL | https://arxiv.org/abs/quant-ph/9811016 |
| DOI | 10.1088/0031-8949/58/5/001 |
| Journal | Phys.Scripta 58 (1998) 417-420 |
Abstract
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schr\"odinger equation. In contradistinction to the "usual'' solitons like {\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to {\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<\pi/(2g), being identically equal to zero for |x-kt|>\pi/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.
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"abstract": "We found a new kind of soliton solutions for the 5-parameter family of the\npotential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the\nSchr\\\"odinger equation. In contradistinction to the \"usual\u0027\u0027 solitons like\n{\\cosh[b(x-kt)]}^{-a}\\exp[i(kx-ft)], the new {\\em Finite-Length Solitons} (FLS)\nare nonanalytical functions with continuous first derivatives, which are\ndifferent from zero only inside some finite regions of space. The simplest\none-dimensional example is the function which is equal to\n{\\cos[g(x-kt)]}^{1+d}\\exp[i(kx-ft)] (with d\u003e0) for |x-kt|\u003c\\pi/(2g), being\nidentically equal to zero for |x-kt|\u003e\\pi/(2g). The FLS exist even in the case\nof a weak nonlinearity, whereas the ``usual\u0027\u0027 solitons exist provided the\nnonlinearity parameters surpass some critical values.",
"arxiv_id": "quant-ph/9811016",
"authors": [
"E. C. Caparelli",
"V. V. Dodonov",
"S. S. Mizrahi"
],
"categories": [
"quant-ph",
"nlin.PS",
"patt-sol"
],
"doi": "10.1088/0031-8949/58/5/001",
"journal_ref": "Phys.Scripta 58 (1998) 417-420",
"title": "Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9811016"
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