Doktorov, Evgeny V.; Molchan, Maxim A. Soliton train dynamics in a weakly nonlocal non-Kerr nonlinear medium. (English) Zbl 1147.35096 J. Phys. A, Math. Theor. 41, No. 31, Article ID 315101, 13 p. (2008). Summary: We analyze chainlike \(N\)-soliton dynamics in a weakly nonlocal, essentially nonintegrable system described by the cubic-quintic nonlinear Schrödinger equation. Quintic nonlinearity is not assumed to be small. This system is reduced to a generalized complex Toda chain model. Numerical simulations demonstrate adverse action of both cubic and quintic nonlocal responses, in their own right, on the quasi-equidistant train propagation, with a development of a chaotic regime. From the Toda chain model, we predict a possibility of mutually compensating both types of nonlocality-induced distortion, restoring thereby a deterministic mode of the train propagation in a weakly nonlocal medium. Analytical predictions corroborate well with numerical results. MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q51 Soliton equations 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems Keywords:nonlinear Schrödinger equation; soliton dynamics; Toda chain model; non-Kerr medium PDFBibTeX XMLCite \textit{E. V. Doktorov} and \textit{M. A. Molchan}, J. Phys. A, Math. Theor. 41, No. 31, Article ID 315101, 13 p. (2008; Zbl 1147.35096) Full Text: DOI