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We develop a theory of soliton spiraling in a bulk nonlinear medium and reveal a new physical mechanism: periodic power exchange via induced coherence, which can lead to stable spiraling and the formation of dynamical two-soliton states.…

We report a theoretical investigation of quadratic frequency combs in a dispersive second-harmonic generation cavity system. We identify different dynamical regimes and demonstrate that the same system can exhibit both bright and dark…

The transition to chaos is ubiquitous in nonlinear systems ranging from fluid dynamics and superconducting circuits to biological organisms. Optical systems driven out of equilibrium such as lasers and supercontinuum generation exhibit…

Real-time spectroscopy based on an emerging time-stretch technique can map the spectral information of optical waves into the time domain, opening several fascinating explorations of nonlinear dynamics in mode-locked lasers. However, the…

Collision refers to a striking nonlinear interaction in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions…

Vector solitons present unique optical pulses characterised by coupled orthogonal polarisation components, offering rich, multidimensional dynamics. Their enhanced degrees of freedom make them highly versatile for exploring nonlinear wave…

We investigate the quench dynamics of a two-component Bose mixture and study the onset of modulational instability, which leads the system far from equilibrium. Analogous to the single-component counterpart, this phenomenon results in the…

We consider the model of a dual-core spatial-domain coupler with chi^(2) and chi^(3) nonlinearities acting in two parallel cores. We construct families of symmetric and asymmetric solitons in the system with self-defocusing chi^(3) terms,…

Using a discrete mode approach we investigate the intermodal dynamics in a frequency comb with nonlinear coupling due to four-wave mixing. In the presence of sufficient saturable absorption, phase space collapses into a single state, and…

Self-sustained oscillations, limit cycles, are a fundamental phenomenon unique to nonlinear dynamic systems of high-dimensional phase space. They enable understanding of a wide range of cyclic processes in natural, social and engineering…

This short review aims to summarize on "What the Charge Density Waves can tell to other inhomogeneous states in strongly correlated systems, particularly to spin-polarized superconductors". We shall update on expanding observations of…

This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…

Over the past decade, cavity solitons have attracted substantial attention for their rich dynamics and their myriad potential applications. Recently, there has been growing interest in understanding cavity solitons in systems of coupled…

It has been established for some time that high-power pump can trap a probe beam of lower intensity that is simultaneously propagating in a Kerr-type optical medium, inducing a focusing of the probe with the emergence of modes displaying…

We discuss soliton control in reconfigurable optically-induced photonic lattices created by three interfering beams. We reveal novel dynamical regimes for strongly localized solitons, including binary switching and soliton revivals through…

We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…

A study is made of frequency comb generation described by the driven and damped nonlinear Schr\"odinger equation on a finite interval. It is shown that frequency comb generation can be interpreted as a modulational instability of the…

Chip-scale integration of optical frequency combs, particularly soliton microcombs, enables miniaturized instrumentation for timekeeping, ranging, and spectroscopy. Although soliton microcombs have been demonstrated on various material…

Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of…

We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in…