Stabilization and destabilization of second-order solitons against perturbations in the nonlinear Schrödinger equation

Hamiltonian form of extended cubic-quintic nonlinear Schrödinger equation in a nonlinear Klein-Gordon model

We derive an extended cubic-quintic nonlinear Schrödinger equation with Hamiltonian structure in a nonlinear Klein-Gordon model with cubic-quintic nonlinearity. We use the nonlinear dispersion relation to properly take into account the input of high-order nonlinear effects in the Hamiltonian perturbation approach to nonlinear modulation. We demonstrate that changing the balance between the cubic and quintic nonlinearities has a significant effect on the stability of unmodulated wave packets to long-wave modulations.

Quantum Fluctuations of the Center of Mass and Relative Parameters of Nonlinear Schrödinger Breathers

We study quantum fluctuations of macroscopic parameters of a nonlinear Schrödinger breather-a nonlinear superposition of two solitons, which can be created by the application of a fourfold quench of the scattering length to the fundamental soliton in a self-attractive quasi-one-dimensional Bose gas. The fluctuations are analyzed in the framework of the Bogoliubov approach in the limit of a large number of atoms N, using two models of the vacuum state: white noise and correlated noise. The latter model, closer to the ab initio setting by construction, leads to a reasonable agreement, within 20% accuracy, with fluctuations of the relative velocity of constituent solitons obtained from the exact Bethe-ansatz results [Phys. Rev. Lett. 119, 220401 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.220401] in the opposite low-N limit (for N≤23). We thus confirm, for macroscopic N, the breather dissociation time to be within the limits of current cold-atom experiments. Fluctuations of soliton masses, phases, and positions are also evaluated and may have experimental implications.

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

We use the ab initio Bethe ansatz dynamics to predict the dissociation of one-dimensional cold-atom breathers that are created by a quench from a fundamental soliton. We find that the dissociation is a robust quantum many-body effect, while in the mean-field (MF) limit the dissociation is forbidden by the integrability of the underlying nonlinear Schrödinger equation. The analysis demonstrates the possibility to observe quantum many-body effects without leaving the MF range of experimental parameters. We find that the dissociation time is of the order of a few seconds for a typical atomic-soliton setting.

Splitting after collision of high-order bright spatial solitons in Kerr media

By numerically studying the collision between (1 + 1)-Dimensional high order bright spatial solitons in a Kerr nonlinear media we show that after the collision, the high order solitons split into a number of first order solitons that corresponds to its order. Two different collision scenarios are considered: collision between two independent high order solitons and a collision with a virtual soliton simulated by the reflection at an angle of a high order soliton at a linear interface. The results demonstrate that in both cases the high order solitons split showing minor differences.

Wave train generation of solitons in systems with higher-order nonlinearities

Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.