Fundamental and Second-Order Superregular Breathers in Vector Fields.

We developed an exact theory of the superregular breathers (SRBs) of Manakov equations. We have shown that the vector SRBs do exist both in the cases of focusing and defocusing Manakov systems. The theory is based on the eigenvalue analysis and on finding the exact links between the SRBs and modulation instability.

Fundamental and second-order dark soliton solutions of two- and three-component Manakov equations in the defocusing regime.

We present exact multiparameter families of soliton solutions for two- and three-component Manakov equations in the defocusing regime. Existence diagrams for such solutions in the space of parameters are presented. Fundamental soliton solutions exist only in finite areas on the plane of parameters.

Extreme spectral asymmetry of Akhmediev breathers and Fermi-Pasta-Ulam recurrence in a Manakov system.

The dynamics of Fermi-Pasta-Ulam (FPU) recurrence in a Manakov system is studied analytically. Exact Akhmediev breather (AB) solutions for this system are found that cannot be reduced to the ABs of a single-component nonlinear Schrödinger equation. Expansion-contraction cycle of the corresponding spectra with an infinite number of sidebands is calculated analytically using a residue theorem.

Q-switching bifurcation dynamics of passively mode-locked lasers.

We model Q-switched pulses in passively mode-locked lasers using the cubic-quintic complex Ginzburg-Landau equation (CGLE). We show that a wide set of parameters of this equation leads to Q-switched pulses of triangular shape that consist of a periodic sequence of evolving dissipative solitons. Bifurcation diagrams demonstrating various transformations of these pulses are calculated in terms of five major parameters of the CGLE.

Exact Analytic Spectra of Asymmetric Modulation Instability in Systems with Self-Steepening Effect.

Nonlinear waves become asymmetric when asymmetric physical effects are present within the system. One example is the self-steepening effect. When exactly balanced with dispersion, it leads to a fully integrable system governed by the Chen-Lee-Liu equation.

Concurrent Passive Mode-Locked and Self-Q-Switched Operation in Laser Systems.

Concurrent passive mode-locked and self-Q-switched operation of laser devices is modeled using the complex cubic-quintic Ginzburg-Landau equation. Experimental observations use a passively mode-locked fiber ring laser with a waveguide array as a fast saturable absorber. The shape of each individual self-Q-switched pulse and the periodic trains of pairs of such pulses are in a good qualitative agreement with the numerical results.

"Extraordinary" modulation instability in optics and hydrodynamics.

The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis.

Complex Korteweg-de Vries equation: A deeper theory of shallow water waves.

Using Levi-Cività's theory of ideal fluids, we derive the complex Korteweg-de Vries (KdV) equation, describing the complex velocity of a shallow fluid up to first order. We use perturbation theory, and the long wave, slowly varying velocity approximations for shallow water. The complex KdV equation describes the nontrivial dynamics of all water particles from the surface to the bottom of the water layer.

Observation of doubly periodic solutions of the nonlinear Schrödinger equation in optical fibers.

We report the first, to the best of our knowledge, experimental observation of doubly periodic first-order solutions of the nonlinear Schrödinger equation in optical fibers. We confirm, experimentally, the existence of -type and -type solutions. This is done by using the initial conditions that consist of a strong pump and two weak sidebands.

Fundamental Peregrine Solitons of Ultrastrong Amplitude Enhancement through Self-Steepening in Vector Nonlinear Systems.

We report the universal emergence of anomalous fundamental Peregrine solitons, which can exhibit an unprecedentedly ultrahigh peak amplitude comparable to any higher-order rogue wave events, in the vector derivative nonlinear Schrödinger system involving the self-steepening effect. We present the exact explicit rational solutions on either a continuous-wave or a periodical-wave background, for a broad range of parameters. We numerically confirm the buildup of anomalous Peregrine solitons from strong initial harmonic perturbations, despite the onset of competing modulation instability.

Super-regular breathers in nonlinear systems with self-steepening effect.

A family of super-regular (SR) breather solutions in systems with self-steepening effect and in the case of either normal or anomalous dispersion is derived analytically. Derivation is based on the Darboux transformation with a quadratic spectral parameter. In contrast to the SR breather solutions in t-symmetric systems such as the nonlinear Schrödinger equation, the new breathers found in the present work evolve asymmetrically even if started from symmetric initial conditions.

Revealing the Transition Dynamics from Q Switching to Mode Locking in a Soliton Laser.

Q switching (QS) and mode locking (ML) are the two main techniques enabling generation of ultrashort pulses. Here, we report the first observation of pulse evolution and dynamics in the QS-ML transition stage, where the ML soliton formation evolves from the QS pulses instead of relaxation oscillations (or quasi-continuous-wave oscillations) reported in previous studies. We discover a new way of soliton buildup in an ultrafast laser, passing through four stages: initial spontaneous noise, QS, beating dynamics, and ML.

Bright and dark rogue internal waves: The Gardner equation approach.

We have found "bright and dark" solutions of the Gardner equation which can model internal rogue waves in three-layer fluids. We provide the first four "bright" and "dark" exact rational solutions to the Gardner equation. These are the lowest-order solutions of the corresponding hierarchies of rogue-wave solutions of this equation.

Shallow-water rogue waves: An approach based on complex solutions of the Korteweg-de Vries equation.

The formation of rogue waves in shallow water is presented in this Rapid Communication by providing the three lowest-order exact rational solutions to the Korteweg-de Vries (KdV) equation. They have been obtained from the modified KdV equation by using the complex Miura transformation. It is found that the amplitude amplification factor of such waves formed in shallow water is much larger than the amplitude amplification factor of those occurring in deep water.

Doubly periodic solutions of the class-I infinitely extended nonlinear Schrödinger equation.

We present doubly periodic solutions of the infinitely extended nonlinear Schrödinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that allows one to vary periods along the two axes. The presence of infinitely many free parameters provides many possibilities in applying the solutions to nonlinear wave evolution.

Directional soliton and breather beams.

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field.

Modulation instability in higher-order nonlinear Schrödinger equations.

We investigate the dynamics of modulation instability (MI) and the corresponding breather solutions to the extended nonlinear Schrödinger equation that describes the full scale growth-decay cycle of MI. As an example, we study modulation instability in connection with the fourth-order equation in detail. The higher-order equations have free parameters that can be used to control the growth-decay cycle of the MI; that is, the growth rate curves, the time of evolution, the maximal amplitude, and the spectral content of the Akhmediev Breather strongly depend on these coefficients.

Dissipative solitons with extreme spikes in the normal and anomalous dispersion regimes.

Prigogine's ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 , 1695-1700 (doi:10.1063/1.

Sasa-Satsuma hierarchy of integrable evolution equations.

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms.

Breather solutions of a fourth-order nonlinear Schrödinger equation in the degenerate, soliton, and rogue wave limits.

We present one- and two-breather solutions of the fourth-order nonlinear Schrödinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions.

Kerr frequency combs and triangular spectra.

Nonlinear externally driven optical cavities are known to generate periodic patterns. They grow from the linearly unstable background states due to modulation instability. These periodic solutions are also known as Kerr frequency combs, which have a variety of applications in metrology.

Positive and negative curvatures nested in an antiresonant hollow-core fiber.

We propose a negative curvature hollow-core fiber that has a nested elliptical element in the antiresonant tubes. The additional elliptical element effectively adds two curvatures, namely, a positive and a negative curvature. Our numerical study shows that it enhances the confinement of the light in the core.

Mid-infrared supercontinuum generation in supercritical xenon-filled hollow-core negative curvature fibers.

We present an investigation on the generation of supercontinuum in the mid-infrared (mid-IR) spectral region. Namely, we study a silica-based anti-resonant hollow-core fiber which has good guidance properties in the mid-IR filled with supercritical xenon providing the necessary high nonlinearity. Our numerical study shows that by launching a 200 nJ pump of 100 fs centered at 3.