1998/11/01 by E. C. Caparelli, E C Caparelli, V. V. Dodonov +3 · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Partial Differential Equations #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.PS #patt-sol #quant-ph
paper · pdf · doi:10.1088/0031-8949/58/5/001
published as Phys.Scripta 58 (1998) 417-420 · 11 pages, LaTex
openalex publication_date 1998/11/01 · arxiv created 1998/11/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 [β( x – kt )] -α exp [i( kx – ω t )], the new 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 [γ( x – kt )] 1+δ exp [i( kx – ω t )] (with δ>0) for | x – kt | <π/2γ, being identically equal to zero for | x – kt | ≥ π/2γ. The FLS exist even in the case of a weak nonlinearity, whereas the "usual" solitons exist provided the nonlinearity parameters surpass some critical values.