Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas.

An asymmetric pair of coupled nonlinear Schrödinger (CNLS) equations has been derived through a multiscale perturbation method applied to a plasma fluid model, in which two wavepackets of distinct (carrier) wavenumbers ([Formula: see text] and [Formula: see text]) and amplitudes ([Formula: see text] and [Formula: see text]) are allowed to co-propagate and interact. The original fluid model was set up for a non-magnetized plasma consisting of cold inertial ions evolving against a [Formula: see text]-distributed electron background in one dimension. The reduction procedure resulting in the CNLS equations has provided analytical expressions for the dispersion, self-modulation and cross-coupling coefficients in terms of the two carrier wavenumbers.

Interactions of solitary waves in the Adlam-Allen model.

We study the interactions of two or more solitary waves in the Adlam-Allen model describing the evolution of a (cold) plasma of positive and negative charges, in the presence of electric and transverse magnetic fields. In order to show that the interactions feature an exponentially repulsive nature, we elaborate two distinct approaches: (a) using energetic considerations and the Hamiltonian structure of the model, and (b) using the so-called Manton method. We compare these findings with results of direct simulations, and we identify adjustments necessary to achieve a quantitative match between them.

Transverse instability and dynamics of nonlocal bright solitons.

We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time-a signature of the transverse instability. The soliton's characteristic timescale associated with its exponential growth is found to depend on the square root of the nonlocality parameter.

Solitary and periodic waves in collisionless plasmas: The Adlam-Allen model revisited.

We consider the Adlam-Allen (AA) system of partial differential equations, which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless plasmas. Here, we identify the solitary waves of the model by implementing a dynamical systems approach. The latter suggests that the model also possesses periodic wave solutions-which reduce to the solitary wave in the limiting case of an infinite period-as well as rational solutions that are obtained herein.

Soliton pairs in two-dimensional nonlocal media.

We study the interaction of optical beams of different wavelengths, described by a two-component, two-dimensional (2D) nonlocal nonlinear Schrödinger (NLS) model. Using a multiscale expansion method the NLS model is asymptotically reduced to the completely integrable 2D Mel'nikov system, the soliton solutions of which are used to construct approximate dark-bright and antidark-bright soliton solutions of the original NLS model; the latter being unique to the nonlocal NLS system with no relevant counterparts in the local case. Direct numerical simulations show that, for sufficiently small amplitudes, both these types of soliton stripes do exist and propagate undistorted, in excellent agreement with the analytical predictions.

Self-similar evolution in nonlocal nonlinear media.

The self-similar propagation of optical beams in a broad class of nonlocal, nonlinear optical media is studied utilizing a generic system of coupled equations with linear gain. This system describes, for instance, beam propagation in nematic liquid crystals and optical thermal media. It is found, both numerically and analytically, that the nonlocal response has a focusing effect on the beam, concentrating its power around its center during propagation.

Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids.

We study a two-dimensional incoherently pumped exciton-polariton condensate described by an open-dissipative Gross-Pitaevskii equation for the polariton dynamics coupled to a rate equation for the exciton density. Adopting a hydrodynamic approach, we use multiscale expansion methods to derive several models appearing in the context of shallow water waves with viscosity. In particular, we derive a Boussinesq/Benney-Luke-type equation and its far-field expansion in terms of Kadomtsev-Petviashvili-I (KP-I) equations for right- and left-going waves.

Interactions and scattering of quantum vortices in a polariton fluid.

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity.

Three-Component Soliton States in Spinor F=1 Bose-Einstein Condensates.

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate.

Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves.

In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events.

Bright and gap solitons in membrane-type acoustic metamaterials.

We study analytically and numerically envelope solitons (bright and gap solitons) in a one-dimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive, and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality.

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments.

Consider a lower-dimensional solitonic structure embedded in a higher-dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space, etc.

From solitons to rogue waves in nonlinear left-handed metamaterials.

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave.

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component.

Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos.

The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson-type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures.

Ring dark and antidark solitons in nonlocal media.

Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form.

Solitons and vortices in two-dimensional discrete nonlinear Schrödinger systems with spatially modulated nonlinearity.

We consider a two-dimensional (2D) generalization of a recently proposed model [Gligorić et al., Phys. Rev.

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.

We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques.

Dark-bright solitons in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

We study a two-component nonlinear Schrödinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component.

Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.

In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates.

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations.

Dark solitons in the presence of higher-order effects.

Dark soliton propagation is studied in the presence of higher-order effects, including third-order dispersion, self-steepening, linear/nonlinear gain/loss, and Raman scattering. It is found that for certain values of the parameters a stable evolution can exist for both the soliton and the relative continuous-wave background. Using a newly developed perturbation theory we show that the perturbing effects give rise to a shelf that accompanies the soliton in its propagation.

Exploring rigidly rotating vortex configurations and their bifurcations in atomic Bose-Einstein condensates.

In the present work, we consider the problem of a system of few vortices N ≤ 5 as it emerges from its experimental realization in the field of atomic Bose-Einstein condensates. Starting from the corresponding equations of motion for an axially symmetric trapped condensate, we use a two-pronged approach in order to reveal the configuration space of the system's preferred dynamical states. We use a Monte Carlo method parametrizing the vortex particles by means of hyperspherical coordinates and identifying the minimal energy ground states thereof for N=2,.