Nonlinearity Management Research Articles

Nonlinearity managed vector solitons

The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the appearance of the effective nonlinear quantum pressure depending on the population of the other component. Using this system of equations, the existence and stability of the vector solitons under the action of the strong nonlinearity management (NM) is investigated. Using a variational approach the parameters of NM vector solitons are found. The numerical simulations of the full time-dependent coupled GPE confirm the theoretical predictions.

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

We consider splitting and stabilization of second-order solitons (2-soliton breathers) in a model based on the nonlinear Schrödinger equation, which includes a small quintic term, and weak resonant nonlinearity management (NLM), i.e., time-periodic modulation of the cubic coefficient, at the frequency close to that of shape oscillations of the 2-soliton. The model applies to the light propagation in media with cubic-quintic optical nonlinearities and periodic alternation of linear loss and gain and to Bose–Einstein condensates, with the self-focusing quintic term accounting for the weak deviation of the dynamics from one dimensionality, while the NLM can be induced by means of the Feshbach resonance. We propose an explanation to the effect of the resonant splitting of the 2-soliton under the action of the NLM. Then, using systematic simulations and an analytical approach, we conclude that the weak quintic nonlinearity with the self-focusing sign stabilizes the 2-soliton, while the self-defocusing quintic nonlinearity accelerates its splitting. It is also shown that the quintic term with the self-defocusing/focusing sign makes the resonant response of the 2-soliton to the NLM essentially broader in terms of the frequency.