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Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation | | E.C.Caparelli
; V.V.Dodonov
; S.S.Mizrahi
; | | Date: |
6 Nov 1998 | | Journal: | Phys.Scripta 58 (1998) 417-420 | | Subject: | Quantum Physics; Pattern Formation and Solitons | quant-ph nlin.PS patt-sol | | Affiliation: | Univ. Federal de Sao Carlos, Brazil | | 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 Schrödinger 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). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual’’ solitons exist provided the nonlinearity parameters surpass some critical values. | | Source: | arXiv, quant-ph/9811016 | | Services: | Forum | Review | PDF | Favorites | |
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