It is shown that the capacity of the channel modeled by (a discretized version of) the stochastic nonlinear Schrödinger (NLS) equation is upper-bounded by logp1` SNRq with SNR “ P0{σ pzq, where P0 is the average input signal power and σpzq is the total noise power up to distance z. The result is a consequence of the fact that the deterministic NLS equation is a Hamiltonian energy-preserving dyn...

We study the solutions of the one dimensional focusing NLS equation. Here we construct new deformations of the Peregrine breather of order 7 with 12 real parameters. We obtain new families of quasirational solutions of the NLS equation. With this method, we construct new patterns of different types of rogue waves. We recover triangular configurations as well as rings isolated. As already seen i...

— We study the cubic non linear Schrödinger equation (NLS) on compact surfaces. On the sphere S 2 and more generally on Zoll surfaces, we prove that, for s > 1/4, NLS is uniformly well-posed in H s , which is sharp on the sphere. The main ingredient in our proof is a sharp bilinear estimate for Laplace spectral projectors on compact surfaces. Résumé. — Onétudie l'´ equation de Schrödinger non l...

In this paper, we review several recent results concerning well-posedness of the one-dimensional, cubic Nonlinear Schrödinger equation (NLS) on the real line R and on the circle T for solutions below the L-threshold. We point out common results for NLS on R and the so-called Wick ordered NLS (WNLS) on T, suggesting that WNLS may be an appropriate model for the study of solutions below L(T). In ...

The adiabatic N-soliton train interactions for the scalar nonlinear Schrö-dinger (NLS) equation and its perturbed versions are well studied. Here we briefly outline how they can be generalized for the higher NLS-type equations and for the multicompo-nent NLS equations. It is shown that in all these cases the complex Toda chain plays fundamental role. 1. Introduction. In a number of applications...

A quintic nonlinear Schrödinger (NLS) equation, with derivative cubic terms, that governs the propagation of nonlinear signals in a nonlinear transmission line (NLTL) is considered. By combining a special phase-imprint transformation with a modified lens transformation, we reduce the equation under consideration to a standard cubic NLS equation with a time-varying gain/loss term and obtain the ...

Applying braided Yang–Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and q-anyonic models as well as nonlinear Schrödinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, N -particle sectors of which yield the well known anyon gases...

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schrödinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the averaged cubic-quintic nonlinear Schrödinger (NLS) equation and modified variational approach for the arrest of collapse coincide. The analytical results are c...

1. Nonlinear Schrödinger equation: setup and applications The nonlinear Schrödinger (NLS) equation [1, 2, 3] is a prototypical dispersive nonlinear partial differential equation (PDE) that has been central for almost four decades now to a variety of areas in Mathematical Physics. It is an equation for a complex field u(x, t) of the form: iu t = −∆u + σ|u| 2 u. u is the complex field whose spati...

The nonlinear Schrödinger (NLS) equation is a popular and relatively simple model used extensively to describe the evolution of nonlinear water-wave groups. It is often applied in relation to the appearance of extremely steep (freak, or rogue) waves in the ocean. The limits of the applicability of the NLS equation, and in particular the relevance of the model to rogue waves, are examined here o...