Elliptic-rogue waves and modulational instability in nonlinear soliton equations.

We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in rational form by elliptic functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds. By refining the modified squared wave function method in tandem with the Darboux-Bäcklund transformation, we establish a quantitative correspondence between elliptic-rogue waves and the modulational instability.

Rogue wave pattern of multi-component derivative nonlinear Schrödinger equations.

This paper studies the multi-component derivative nonlinear Schrödinger (n-DNLS) equations featuring nonzero boundary conditions. Employing the Darboux transformation method, we derive higher-order vector rogue wave solutions for the n-DNLS equations. Specifically, we focus on the distinctive scenario where the (n+1)-order characteristic polynomial possesses an explicit (n+1)-multiple root.

Phase characters of optical dark solitons with third-order dispersion and delayed nonlinear response.

Dark soliton is usually seen as one of the simplest topological solitons, due to phase shift across its intensity dip. We investigate phase characters of single-valley dark soliton (SVDS) and double-valley dark soliton (DVDS) in a single-mode optical fiber with third-order dispersion and delayed nonlinear response. Notably, two different phase shifts can produce an SVDS with the same velocity under some conditions, which is not admitted for a dark soliton with only the second-order dispersion and self-phase modulation, whose phase shift and velocity is a one-to-one match.

Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning.

Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves (RWs), due to modulational instability. Numerical simulations showed that these RWs seemed to have similar unit structure. However, to the best of our knowledge, there are no relative results to prove that these RWs have the similar patterns for different perturbations, partly due to that it is hard to measure the RW pattern automatically.

Clustered piperidinium-functionalized poly(terphenylene) anion exchange membranes with well-developed conductive nanochannels.

Anion exchange membrane fuel cells (AEMFCs) attract considerable attention owing to their high-power density and potential utilization of cheap non-noble metal catalysts. However, anion exchange membranes (AEMs) still face the problems of low conductivity, poor dimensional and chemical stability. To address these issues, AEMs with clustered piperidinium groups and ether-bond-free poly(terphenylene) backbone (3QPAP-x, x = 0.

Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions.

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range [0,2π], which is quite different from that of the usual single-valley dark soliton.

Parity-time-symmetric rational vector rogue waves of the n-component nonlinear Schrödinger equation.

Extreme events are investigated in the integrable n-component nonlinear Schrödinger (NLS) equation with focusing nonlinearity. We report novel multi-parametric families of rational vector rogue wave (RW) solutions featuring the parity-time ( PT) symmetry, which are characterized by non-identical boundary conditions for the components that are consistent with the degeneracy of n branches of Benjamin-Feir instability. Explicit examples of PT-symmetric rational vector RWs are presented.

Coupling hollow FeO nanoparticles with oxygen vacancy on mesoporous carbon as a high-efficiency ORR electrocatalyst for Zn-air battery.

Designing a low-cost, high-efficiency and robust doped-carbon-based oxygen reduction reaction electrocatalyst for large-scale implementations of fuel cells is highly desirable but challenging. In this work, we report a new type of hollow FeO with oxygen vacancy incorporating on mesoporous carbon prepared by pyrolyzing mesoporous carbon enriched with oxygen-containing functional groups, in combination with ferric acetylacetonate. The catalysts possess high specific surface area with predominantly mesoporous architecture and ultrahigh nitrogen content (up to 7.

Nondegenerate bound-state solitons in multicomponent Bose-Einstein condensates.

We investigate nondegenerate bound-state solitons systematically in multicomponent Bose-Einstein condensates, through developing the Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound states in effective quantum wells, in sharp contrast to the bright solitons and dark solitons reported before (which usually correspond to ground state and free state, respectively). We further demonstrate that bound-state solitons with nodes are induced by incoherent superposition of solitons in different components.

Mechanism of Kuznetsov-Ma breathers.

We discuss how to understand the dynamical process of Kuznetsov-Ma breather, based on some basic physical mechanisms. It is shown that the dynamical process of Kuznetsov-Ma breather involves at least two distinctive mechanisms: modulational instability and the interference effects between a bright soliton and a plane-wave background. Our analysis indicates that modulational instability plays dominant roles in the mechanism of Kuznetsov-Ma breather admitting weak perturbations, and the interference effect plays a dominant role for the Kuznetsov-Ma breather admitting strong perturbations.

3D Electronic Channels Wrapped Large-Sized Na V (PO ) as Flexible Electrode for Sodium-Ion Batteries.

The development of portable and wearable electronics has aroused the increasing demand for flexible energy-storage devices, especially for the characteristics of high energy density, excellent mechanical properties, simple synthesis process, and low cost. However, the development of flexible electrodes for sodium-ion batteries (SIBs) is still limited due to the intricate production methods and the relatively high-cost of current collectors such as graphene/graphene oxide and carbon nanotubes. Here, the hierarchical 3D electronic channels wrapped large-sized Na V (PO ) is designed and fabricated by a simple electrospinning technique.

Remarkable Effect of Sodium Alginate Aqueous Binder on Anatase TiO as High-Performance Anode in Sodium Ion Batteries.

Sodium alginate (SA) is investigated as the aqueous binder to fabricate high-performance, low-cost, environmentally friendly, and durable TiO anodes in sodium-ion batteries (SIBs) for the first time. Compared to the conventional polyvinylidene difluoride (PVDF) binder, electrodes using SA as the binder exhibit significant promotion of electrochemical performances. The initial Coulombic efficiency is as high as 62% at 0.

Quick Activation of Nanoporous Anatase TiO as High-Rate and Durable Anode Materials for Sodium-Ion Batteries.

To understand the slow capacity activation behavior of anatase TiO as a sodium-ion battery anode during cycling, a nanoporous configuration was designed and prepared. On the basis of the comprehension of the Na-ion storage mechanism, the behavior is demonstrated to be related with the gradual formation of amorphous phase resulting from the phase transition during discharge. In addition, the level of phase transition is determined by the discharge rates and cycle numbers, which strongly affects the electrochemical performance of anatase TiO.

Generation mechanisms of fundamental rogue wave spatial-temporal structure.

We discuss the generation mechanism of fundamental rogue wave structures in N-component coupled systems, based on analytical solutions of the nonlinear Schrödinger equation and modulational instability analysis. Our analysis discloses that the pattern of a fundamental rogue wave is determined by the evolution energy and growth rate of the resonant perturbation that is responsible for forming the rogue wave. This finding allows one to predict the rogue wave pattern without the need to solve the N-component coupled nonlinear Schrödinger equation.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.

Defocusing complex short-pulse equation and its multi-dark-soliton solution.

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation.

W-shaped solitons generated from a weak modulation in the Sasa-Satsuma equation.

We study rational solutions of continuous wave backgrounds with the critical frequencies of the Sasa-Satsuma equation, which can be used to describe the evolution of the optical field in a nonlinear fiber with some high-order effects. We find a striking dynamical process that two W-shaped solitons are generated from a weak modulation signal on the continuous wave backgrounds. This provides a possible way to obtain stable high-intensity pulses from a low-intensity continuous wave background.

Vector bright solitons associated with positive coherent coupling via Darboux transformation.

Describing coherently coupled and orthogonally polarized waveguide modes in the Kerr medium, vector bright solitons associated with positive coherent coupling are studied in this paper. Some conserved quantities and infinitely many conservation laws are computed, and the existence of Lax pair indicates the integrability of the two-coupled nonlinear Schrödinger system with positive coherent coupling. Performing the iterative algorithm of Darboux transformation, we present formulas of one-, two-, and even N-soliton solutions.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation.

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation.

We investigate the solution in rational form for the Sasa-Satsuma equation on a continuous background which describes a nonlinear fiber system with higher-order effects including the third-order dispersion, Kerr dispersion, and stimulated inelastic scattering. The W-shaped soliton in the system is obtained analytically. It is found that the height of hump for the soliton increases with decreasing the background frequency in certain parameter regime.

High-order rogue waves in vector nonlinear Schrödinger equations.

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions.

Simple determinant representation for rogue waves of the nonlinear Schrödinger equation.

We present a simple representation for arbitrary-order rogue wave solution and a study on the trajectories of them explicitly. We find that the trajectories of two valleys on whole temporal-spatial distribution all look "X" -shaped for rogue waves. Additionally, we present different types of high-order rogue wave structures, which could be helpful towards realizing the complex dynamics of rogue waves.

4-Nitro-3-(5-tetrazole)furoxan and its salts: synthesis, characterization, and energetic properties.

A series of new energetic salts based on 4-nitro-3-(5-tetrazole)furoxan (HTNF) has been synthesized. All of the salts have been fully characterized by nuclear magnetic resonance ((1)H and (13)C), infrared (IR) spectroscopy, elemental analysis, and differential scanning calorimetry (DSC). The crystal structures of neutral HTNF (3) and its ammonium (4) and N-carbamoylguanidinium salts (9) have been determined by single-crystal X-ray diffraction analysis.

Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.

In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation.

Phasic respiratory modulation of pharyngeal collapsibility via neuromuscular mechanisms in rats.

Obstructive sleep apnea patients experience recurrent upper airway (UA) collapse due to decreases in the UA dilator muscle activity during sleep. In contrast, activation of UA dilators reduces pharyngeal critical pressure (Pcrit, an index of pharyngeal collapsibility), suggesting an inverse relationship between pharyngeal collapsibility and dilator activity. Since most UA muscles display phasic respiratory activity, we hypothesized that pharyngeal collapsibility is modulated by respiratory drive via neuromuscular mechanisms.