Thermal field soliton self-organization arising due to absorption of background atoms vibrations is observed in numerical experiment in nonlinear chain with Lennard-Jones potential at high temperature. At some stage intensive space-localized waves are formed and give additional peaks on high-energy tile of energy distribution unlike of Gibbs one.
We show that self-organization occurs in the phase dynamics of soliton modelocking in paramet- ric frequency combs. Reduction of the Lugiato-Lefever equation (LLE) to a simpler set of phase equations reveals that this self-organization arises via mechanisms akin to those in the Kuramoto model for synchronization of coupled oscillators. In addition, our simulations show that the phase equations evolve to a broadband phase-locked state, analogous to the soliton formation process in the LLE. Our simplified equations intuitively explain the origin of the pump phase offset in soliton- modelocked parametric frequency combs. They also predict that the phase of the intracavity field undergoes an anti-symmetrization that precedes phase synchronization, and they clarify the role of chaotic states in soliton formation in parametric combs.
We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equation, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg de Vries equation. The results show that deep learning method can solve the high-order nonlinear soliton equation and reveal the interaction between solitons.
We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrodinger operator associated with the KdV soliton gas dynamics. As a by-product of our derivation we find the speed of sound in the soliton gas with Gaussian spectral distribution function.
The scattering of a linear wave on an optical event horizon, induced by a cross polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with co-polarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent on the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations using two coupled full vectorial nonlinear Schrodinger equations fully support the experimental results.
We study the interactions of a Bragg-grating soliton with a localized attractive defect which is a combined perturbation of the grating and refractive index. A family of exact analytical solutions for solitons trapped by the delta-like defect is found. Direct simulations demonstrate that, up to the numerical accuracy available, the trapped soliton is stable at a single value of its intrinsic parameter (mass). Trapped solitons with larger mass relax to the stable one through the emission of radiation, while the solitons with smaller mass decay. Depending on values of parameters, simulations of collisions between moving solitons and the defect show that the soliton can get captured, pass through, or even bounce from the defect. If the defect is strong and the soliton is heavy enough, it may split, as a result of the collision, into three fragments: trapped, transmitted, and reflected ones.