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We address the degree of universality of the Fermi-Pasta-Ulam recurrence induced by multisoliton fission from a harmonic excitation by analysing the case of the semiclassical defocusing nonlinear Schrodinger equation, which models nonlinear wave propagation in a variety of physical settings. Using a suitable Wentzel-Kramers-Brillouin approach to the solution of the associated scattering problem we accurately predict, in full analytical way, the number and the features (amplitude and velocity) of soliton-like excitations emerging post-breaking, as a function of the dispersion smallness parameter. This also permits to predict and analyse the near-recurrences, thereby inferring the universal character of the mechanism originally discovered for the Korteweg-deVries equation. We show, however, that important differences exist between the two models, arising from the different scaling rules obeyed by the soliton velocities.
By using the Darboux transformation, we obtain two new types of exponential-and-rational mixed soliton solutions for the defocusing nonlocal nonlinear Schrodinger equation. We reveal that the first type of solution can display a large variety of inte
Solitons on a finite a background, also called breathers, are solutions of the focusing nonlinear Schrodinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes Akhmediev bre
We present doubly-periodic solutions of the infinitely extended nonlinear Schrodinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that allows to
We consider an integrable generalization of the nonlinear Schrodinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way that the Camassa Holm equa
In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirotas bilinear method. One- and two-bright-dark soliton solutions are explicitly presented for two-