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Soliton train dynamics in a weakly nonlocal non-Kerr nonlinear medium. (English) Zbl 1147.35096

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
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