Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

We consider a higher-order Chen-Lee-Liu (CLL) equation with third order dispersion and quintic nonlinearity terms. In the framework of the Riemann-Hilbert method, we obtain the compact N-soliton formula expressed by determinants. Based on the determinant solution, some properties for single soliton and asymptotic analysis of N-soliton solution are explored. The simple elastic interaction of N solitons is confirmed.     

Multisoliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Schrödinger equation from plasma physics, arterial mechanics, fluid dynamics and optical communications

In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schrödinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Bäcklund transformation transforms between (N − 1)- and N-soliton solutions.     

Multisoliton solutions of the (2+1)-dimensional Harry Dym equation

The exact N-soliton solutions of the (2+1)-dimensional Harry Dym equation are constructed analytically. Different types of two-soliton interactions are singled out in the general N-soliton solution. The existence of inelastic soliton interaction and two-soliton resonances are shown.     

Detecting identical entanglement pure states for two qubits

In this paper, investigation is made on a Kadomtsev–Petviashvili-based system, which can be seen in fluid dynamics, biology and plasma physics. Based on the Hirota method, bilinear form and Bäcklund transformation (BT) are derived. N-soliton solutions in terms of the Wronskian are constructed, and it can be verified that the N-soliton solutions in terms of the Wronskian satisfy the bilinear form and Bäcklund transformation. Through the N-soliton solutions in terms of the Wronskian, we graphically obtain the kink-dark-like solitons and parallel solitons, which keep their shapes and velocities unchanged during the propagation.     

General N-soliton solution of the AKNS class on arbitrary background

An explicit determinant formula for the N-fols Bäcklund transform of any pair of AKNS fields q(x, t), r(x, t) is derived. In particular this formula includes all N-soliton solutions of nonlinear evolution equations which belong to the AKNS class.     

Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics

In this Letter, the Exp-function method is generalized to construct N-soliton solutions of a KdV equation with variable coefficients. As a result, 1-soliton, 2-soliton and 3-soliton solutions are obtained, from which the uniform formula of N-soliton solutions is derived. It is shown that the Exp-function method may provide us with a straightforward and effective mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics.     

Effect of 50 MeV Li+3 and 80 MeV C+5 ions’ beam irradiation on the optical,structural, chemical and surface topographic properties of PMMA films*

The self-standing films of polymethyl methacrylate (PMMA) were irradiated under vacuum with 50?MeV lithium (Li³⁺) and 80?MeV carbon (C⁵⁺) ions to the fluences of 3?×?10¹⁴, 1?×?10¹⁵, 1?×?10¹⁶ and 1?×?10¹⁷ ions µm^?2. The pristine and irradiated samples of PMMA films were studied by using ultraviolet–visible (UV–Vis) spectrophotometry, Fourier transform infrared, X-ray diffractrometer and atomic force microscopy. With increasing ion fluence of swift heavy ion (SHI), PMMA suffers degradation, UV–Vis spectra show a shift in the absorption band from the UV towards visible, attributing the formation of the modified system of bonds. E_g and E_a decrease with increasing ion fluence. The size of crystallite and crystallinity percentage decreases with increasing ion fluence. With SHI irradiation, the intensity of IR bands and characteristic bands of different functional groups are found to shift drastically. The change in (E_g) and (N) in carbon cluster is calculated. Shifting of the absorption band from the UV towards visible along with optical activity and as a result of irradiation, some defects are created in the polymer causing the formation of conjugated bonds and carbon clusters in the polymer, which in turn lead to the modification in optical properties that could be useful in the fabrication of optoelectronic devices, gas sensing, electromagnetic shielding and drug delivery.     

The AB Equations and the ∂ ̄ -dressing Method in Semi-Characteristic Coordinates

The dressing method based on the 2 × 2 matrix \(\bar \partial \) -problem is generalized to study the canonical form of AB equations. The soliton solutions for the AB equations are given by virtue of the properties of Cauchy matrix. Asymptotic behaviors of the N-soliton solution are discussed.     

Conservation laws,solitons, breather and rogue waves for the (2+1)-dimensional variable-coefficient Nizhnik–Novikov–Veselov system in an inhomogeneous medium

In this paper, we consider the (2+1)-dimensional variable-coefficient Nizhnik–Novikov–Veselov system in an inhomogeneous medium, which is the isotropic Lax integrable extension of the Korteweg-de Vries equation. Infinitely-many conservation laws are constructed. N-soliton solutions in terms of the Wronskian are obtained via the Hirota method. Velocity and shape of the soliton can be influenced by those variable coefficients, while the amplitude of the soliton can not be affected. Collision between the two solitons is shown to be elastic. Breather wave solutions are constructed via the trilinear method. Such phenomena as the deceleration and compression of the breather waves are studied graphically. Rogue wave solutions are derived when the periods of the breather wave solutions go to the infinity. Separated and united composite rogue waves are discussed graphically.     

Excitation and Emission Spectra of Cs2NaLnCl6 Crystals Using Synchrotron Radiation

ABSTRACT

The visible emission and vacuum ultraviolet excitation spectra of the series Cs₂NaLnCl₆ (Ln = Y, Nd, Sm, Eu, Tb, Er, Yb) and Cs₂NaYCl₆:Ln³⁺ (Ln = Sm, Er) have been recorded using synchrotron radiation at room temperature, and in some cases at 10 K. The excitation spectra comprise features associated with charge transfer, excitation from the valence to conduction band, and impurity bands. No d–f emissions were observed for these Ln³⁺ ions, so that the emission bands comprise intraconfigurational 4f ^N –4f ^N transitions and impurity bands, whose natures are discussed. Theoretical simulations of the f–d absorption spectra have been included. The comparison with data from the synchrotron at Desy enables a comprehensive account of the ground (or vibrationally excited ground for Ln²⁺) states of the Ln³⁺ 4f ^N , Ln³⁺ 4f ^N?15d, and Ln²⁺ 4f ^N+1 configurations relative to the valence and conduction bands of Cs₂NaLnCl₆, for which the band gaps are between 6.6 and 8.1 eV.     

A Highly Sensitive and Selective Fluorescent Chemodosimeter for Hg<Superscript>2+</Superscript> in Neutral Aqueous Solution

A fluorescent assay of Hg²⁺ in neutral aqueous solution was developed using N-[p-(dimethylamino)benzamido]-N′-phenylthiourea (1). 1’s fluorogenic chemodosimetric behaviors towards various metal ions were studied and a high sensitivity as well as selectivity was achieved for Hg²⁺. It was because of a strongly fluorescent 1,3,4-oxadiazoles which was produced by the Hg²⁺ promoted desulfurization reaction. The spectra of ESI mass and IR provided evidences for this reaction. According to fluorescence titration, a good linear relationship ranging from 1.0 × 10⁻⁷ to 2.0 × 10⁻⁵ mol l⁻¹ was obtained with the limit of detection as 3.1 × 10⁻⁸ mol l⁻¹. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The SN3–SN2 spectrum. Rate constants and product selectivities for solvolyses of benzenesulfonyl chlorides in aqueous alcohols

Rate constants for a wide range of binary aqueous mixtures and product selectivities (S) in ethanol–water (EW) and methanol–water (MW) mixtures, are reported at 25 °C for solvolyses of benzenesulfonyl chloride and the 4‐chloro‐derivative. S is defined as follows using molar concentrations: S = ([ester product]/[acid product]) × ([water solvent]/[alcohol solvent]). Additional selectivity data are reported for solvolyses of 4‐Z‐substituted sulfonyl chlorides (Z = OMe, Me, H, Cl and NO₂) in 2,2,2‐trifluoroethanol–water. To explain these results and previously published data on kinetic solvent isotope effects (KSIEs) and on other solvolyses of 4‐nitro and 4‐methoxybenzenesulfonyl chloride, a mechanistic spectrum involving a change from third order to second order is proposed. The molecularity of these reactions is discussed, along with new term ‘S_N3–S_N2 spectrum’ and its connection with the better established term ‘S_N2–S_N1 spectrum’. Copyright © 2009 John Wiley & Sons, Ltd.     

Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma

In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.     

Types of two-dimensionalN = 4 superconformal field theories

Various types ofN = 4 superconformal symmetries in two dimensions are considered. It is proposed that apart from the well-known cases ofSU (2)and SU(2) × SU(2) ×U (1), their Kac-Moody symmetry can also be SU(2) × (U (1))⁴. Operator product expansions for the last case are derived. A complete free field realization for the same is obtained     

Casorati determinant solution for the discrete-time relativistic Toda lattice equation

The discrete-time relativistic Toda lattice (dRTL) equation is investigated by using the bilinear formalism. Bilinear equations are systematically constructed with the aid of the singularity confinement method. It is shown that the dRTL equation is decomposed into the Bäcklund transformations of the discrete-time Toda lattice equation. The N-soliton solution is explicitly constructed in the form of the Casorati determinant.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Effect of atmospheric pressure pulsed discharge spatial inhomogeneity on Ar I and H I lines: Electron number density study

The spatial inhomogeneity of pulsed atmospheric pressure discharge in argon is investigated using the electron number density N_e diagnostics procedure applied to asymmetrically broadened Ar I lines. A dedicated fitting procedure is used for describing Ar I 703.0 nm line shape recorded from argon gas discharge and H I (at 486.13 and 656.28 nm) lines recorded from Ar-H₂ gas mixture discharge. The results revealed the change in N_e in both axial and radial directions. The additional Ar I lines at 614.5, 710.7, 731.2, and 731.6 nm, recorded from integral spatial radiation, are analysed as well to confirm the results from the plasma column region. The possibility of using AlO (B²∑⁺–X²∑⁺) and CN (B²∑⁺–X²∑⁺) molecular bands for gas temperature T_g measurements in this type of gas discharge source is demonstrated and T_g used as an input parameter for the N_e diagnostics procedure. For the proper identification of molecular band spectral lines, the Fortrat parabolas are constructed. The results obtained from Ar I 703.0 nm line indicate three different N_e values, with N_e1 ≈ 0.6 × 10¹⁶ cm⁻³, N_e2 ≈ 3.6 × 10¹⁶ cm⁻³, and N_e3 ≈ 19 × 10¹⁶ cm⁻³ measured from the plasma column. These N_e values increase in the cathode and anode region.     

Break up of bound-N-spatial-soliton in a ramp waveguide

We present an analytical and numerical investigation of the propagation of spatial solitons in a nonlinear waveguide with ramp linear refractive index profile (ramp waveguide). For the propagation of a single soliton beam in a ramp waveguide, the particle theory shows that the soliton beam follows a parabolic curve in the region where the linear refractive index increases and a straight line outside the waveguide. The acceleration of the soliton depends on the beam intensity: higher amplitude solitons experience higher acceleration. Numerical calculations using an implicit Crank–Nicolson scheme confirm the result of the particle theory. Combining these propagation properties with the theory about bound-N-soliton, we study the break up of such a bound-N-soliton in a ramp waveguide. In a ramp waveguide, a bound-N-soliton will always be splitted into N independent solitons with the higher amplitude soliton emitted first. The amplitude of the separated solitons after break up are calculated using the soliton theory as if the solitons are independent. Numerical simulations show that the results agree quite well with this theoretical prediction, indicating that the interaction during break up has only little influence.     

Absolute cross sections of electron attachment to molecular clusters. Part II: Formation of (H2O) N? , (N2O) N? , and (N2) N?

Absolute cross sections σ⁻(E, N) of electron attachment to clusters (H₂O) _N , (N₂O) _N , and (N₂) _N for varying electron energy E and cluster size N are measured by using crossed electron and cluster beams in a vacuum. Continua of σ⁻(E) are found that correlate well with the functions of electron impact excitation of molecules’ internal degrees of freedom. The electron is attached through its solvation in a cluster. In the formation of (H₂O) _N ⁻ , (N₂O) _N ⁻ , and (N₂) _N ⁻ , the curves σ⁻(N) have a well-defined threshold because of a rise in the electron thermalization and solvation probability with N. For (H₂O)₉₀₀, (N₂O)₃₅₀, and (N₂)₂₆₀ clusters at E = 0.2 eV, the energy losses by the slow electron in the cluster are estimated as 3.0 × 10⁷, 2.7 × 10⁷, and 6.0 × 10⁵ eV/m, respectively. It is found that the growth of σ⁻ with N is the fastest for (H₂O) _N and (N₂) _N clusters at E → 0 as a result of polarization capture of the s-electron. Specifically, at E = 0.1 eV and N = 260, σ⁻ = 3.0 × 10⁻¹³ cm² for H₂O clusters, 8.0 × 10⁻¹⁴ cm² for N₂O clusters, and 1.4 × 10⁻¹⁵ cm² for N₂ clusters; at E = 11 eV, σ⁻ = 9.0 × 10⁻¹⁶ cm² for (H₂O)₂₀₀ clusters, 2.4 × 10⁻¹⁴ cm² for (N₂O)₃₅₀ clusters, and 5.0 × 10⁻¹⁷ cm² for (N₂)₂₆₀ clusters; finally, at E = 30 eV, σ⁻ = 3.6 × 10⁻¹⁷ cm² for (N₂O)₁₀ clusters and 3.0 × 10⁻¹⁷ cm² for (N₂)₁₂₅ clusters. Original Russian Text ? A.A. Vostrikov, D.Yu. Dubov, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 12, pp. 1–15.     

The chemisorption of N2 on the (110) surface of iridium

The molecular chemisorption of N₂ on the reconstructed Ir(110)-(1 × 2) surface has been studied with thermal desorption mass spectrometry, XPS, UPS, AES, LEED and the co-adsorption of N₂ with hydrogen. Photoelectron spectroscopy shows molecular levels of N₂ at 8.0 (5σ + 1π) and 11.8 (4σ) eV in the valence band and at 399.2 eV with a satellite at 404.2 eV in the N(1s) region, where the binding energies are referenced to the Ir Fermi level. The kinetics of adsorption and desorption show that both precursor kinetics and interadsorbate interactions are important for this chemisorption system. Adsorption occurs with a constant probability of adsorption of unity up to saturation coverage (4.8 × 10¹⁴ cm^?2), and the thermal desorption spectra give rise to two peaks. The activation energy for desorption varies between 8.5 and 6.0 kcal mole^?1 at low and high coverages, respectively. Results of the co-adsorption of N₂ and hydrogen indicate that adsorbed N₂ resides in the missing-row troughs on the reconstructed surface. Nitrogen is displaced by hydrogen, and the most tightly bound state of hydrogen blocks virtually all N₂ adsorption. A p1g1(2 × 2) LEED pattern is associated with a saturated overlayer of adsorbed N₂ on Ir(110)-(1 × 2).