We numerically investigate self-frequency blueshifting of a fundamental soliton in a gas-filled hollow-core photonic crystal fiber. Because of the changing underlying soliton parameters, the blueshift gives rise to adiabatic soliton compression. Based on these features, we propose a device that enables frequency shifting over an octave and pulse compression from 30 fs down to 2.3 fs.

A connection is established between the soliton equations and curves moving in a three dimensional space V3. The sign of the selfinteracting terms of the soliton equations are related to the signature of V3. It is shown that there corresponds a moving curve to each soliton equations.

Soliton automata are the mathematical models of certain possible molecular switching devices called soliton circuits. Both from theoretical and practical point of view, it is a central question to describe soliton automata with a single external vertex. Extending a result of Dassow and Jürgensen, we characterize nondeterministic automata in this special case.

We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg-de Vries 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.

We study the traveling waves of the Nonlinear Schrödinger Equation in dimension one. Through various model cases, we show that for nonlinearities having the same qualitative behaviour as the standard Gross-Pitaevkii one, the traveling waves may have rather different properties. In particular, our examples exhibit multiplicity or nonexistence results, cusps (as for the Jones-Roberts curve in the...

We show that a single dark soliton can exist in a spin-orbit-coupled Fermi gas with a high spin imbalance, where spin-orbit coupling favors uniform superfluids over nonuniform Fulde-Ferrell-Larkin-Ovchinnikov states, leading to dark soliton excitations in highly imbalanced gases. Above a critical spin imbalance, two topological Majorana fermions without interactions can coexist inside a dark so...

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle ’living’ under the influence of a complicated potential which is a function...

We study the dynamics of the soliton–radiation interaction in the process of soliton excitation in quadratic nonlinear media. The focus is on the dynamics of initial signals that are not weakly perturbed exact solitons. We use a combination of numerical experiments and analytical tools based on the integral conserved quantities of the wave evolution. We show the rate of convergence of represent...

The relationship between the soliton dynamics provided by the classical sine-Gordon and massive Thirring models is exhibited. Solitons are characterized as classical relativistic particles through the consideration of their associated canonical realizations of the Poincare group. It is shown that the soliton in the massive Thirring model determines two different kinds of relativistic particles ...