New Exact Solution of (N+1)-Dimensional Burgers System

In this letter, using a Bäcklund transformation and the new variable separation approach, we find a new general solution of the (N+1)-dimensional Burgers system. The form of the universal formula obtained from many (2+1)-dimensional system is extended.     

Hydrogen adsorption and diffusion on Pd(1 1 1)

The adsorption, diffusion and ordering of hydrogen on Pd(1 1 1) was studied by scanning tunneling microscopy in the temperature range of 37-90 K. At low coverage isolated hydrogen atoms were observed. They formed √3×√3-1H islands as the coverage increased. Above 1/3 monolayer (ML) coverage areas of a new phase with √3×√3-2H structure were formed, with both structures coexisting between 1/3 and 2/3 ML. Finally a 1 × 1 structure was formed after high exposures of hydrogen above 50 K, with a coverage close to 1 ML. Atomically resolved images reveal that H binds to fcc hollow sites.     

Degeneracy pressure of electrons: a new effect for Pb islands grown on Si(1 1 1) substrate

We have found that the degeneracy pressure of electrons (DPE) inside Pb islands grown on a silicon substrate plays a crucial role in stabilizing the islands. In most cases, at a metal-semiconductor interface charge spilling takes place due to the difference of Fermi energies between the two materials, which makes DPE decrease along with the energy of the system. Based on this new effect, calculations of energy as a function of height are carried out for Pb islands grown on Si(1 1 1)-() and -(7 × 7) phases, which have most stable heights of 5 and 7 monolayers (ML), respectively. Our results explain why these most stable heights are observed. Using this new effect supplemented with experimental data, all the preferred heights of the Pb islands on Si(1 1 1)-(7 × 7) can be explained too.     

Two series of triple- and single-domain reconstructions induced by europium on vicinal Si(1 1 1) [ ]-miscut surface

The growth and properties of Eu-induced one-dimensional reconstructions on vicinal Si(1 1 1) surface miscut in the [ ] direction have been studied by low energy electron diffraction and scanning tunneling microscope in the submonolayer range. The focus has been attended to the formation of single-domain structures and the influence of preparation parameters on the domain orientation. We have found the critical conditions for the preparation of a variety of Eu-induced single-domain (n×2) and (n×1) structures. In addition, a new intermediate phase showing the 9×1 periodicity between 3×2 and 2×1 phases is detected.     

New Bilinear Bäcklund Transformation and Higher Order Rogue Waves with Controllable Center of a Generalized (3+1)-Dimensional Nonlinear Wave Equation

In this paper, we first obtain a bilinear form with small perturbation u_0 for a generalized(3+1)-dimensional nonlinear wave equation in liquid with gas bubbles. Based on that, a new bilinear B?cklund transformation which consists of four bilinear equations and involves seven arbitrary parameters is constructed. After that, by applying a new symbolic computation method, we construct the higher order rogue waves with controllable center to the generalized(3+1)-dimensional nonlinear wave equation. The rogue waves present new structure, which contain two free parametersα and β. The dynamic properties of the higher order rogue waves are demonstrated graphically. The graphs tell that the parameters α and β can control the center of the rogue waves.     

The local structure of SO2 and SO3 on Ni(1 1 1)

The normal incidence X-ray standing wave (NIXSW) technique, supported by X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure (NEXAFS), has been used to determine the local adsorption geometry of SO₂ and SO₃ on Ni(1 1 1). Chemical-state specific NIXSW data for coadsorbed SO₃ and S, formed by the disproportionation of adsorbed SO₂ after heating from 140 K to 270 K, were obtained using S 1s photoemission detection. For adsorbed SO₂ at 140 K the new results confirm those of an earlier study [Jackson et al., Surf. Sci. 389 (1997) 223] that the molecule is located above hollow sites with its molecular plane parallel to the surface and the S and O atoms in off-atop sites; corrections to account for the non-dipole effects in the interpretation of the NIXSW monitored by S 1s and O 1s photoemission, not included in the earlier work, remove the need for any significant adsorption-induced distortion of the SO₂ in this structure. SO₃, not previously investigated, is found to occupy an off-bridge site with the C_3v axis slightly tilted relative to the surface normal and with one O atom in an off-atop site and the other two O atoms roughly between bridge and hollow sites. The O atoms are approximately 0.87 Å closer to the surface than the S atom. This general bonding orientation for SO₃ is similar to that found on Cu(1 1 1) and Cu(1 0 0) both experimentally and theoretically, although the detailed adsorption sites differ.     

New Double-Periodic Soliton Solutions for the (2+1)-Dimensional Breaking Soliton Equation

Under investigation is the (2+1)-dimensional breaking soliton equation. Based on a special ansätz functions and the bilinear form, some entirely new double-periodic soliton solutions for the (2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures.     

Multi-linear Variable Separation Approach to Solve a (2+1)-Dimensional Generalization of Nonlinear Schrödinger System

By using a Bäcklund transformation and the multi-linear variable separation approach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinear Schrödinger system. The new “universal” formula is defined, and then, rich coherent structures can be found by selecting corresponding functions appropriately.     

New lump,lump-kink,breather waves and other interaction solutions to the (3+1)-dimensional soliton equation

This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution's visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.     

Overpotential deposition of Ag monolayer and bilayer on Au(1 1 1) mediated by Pb adlayer underpotential deposition/stripping cycles

Ultra-thin Ag films on the Au(1 1 1) surface were prepared via overpotential deposition (OPD) in the presence of Pb²⁺ ions. By carrying out repetitive Pb adlayer underpotential deposition (UPD) and stripping cycles during Ag bulk deposition, the two-dimensional growth of Ag films was significantly enhanced in high OPD. The Ag monolayer sample was made by comparing the voltammetry curves, in which the signatures for Pb adlayer UPD on Au(1 1 1) changed to that on Ag(1 1 1). As demonstrated by the X-ray specular reflectivity measurements, nearly complete monolayer and bilayer films can be made with optimized deposition procedures. On subatomic scale, however, we found that these films have significant higher root-mean-square displacement amplitudes than those underpotentially deposited Ag monolayer and bilayer on either Au(1 1 1) or Pt(1 1 1).     

Darboux Transformations,Higher-Order Rational Solitons and Rogue Wave Solutions for a(2+1)-Dimensional Nonlinear Schrdinger Equation

By Taylor expansion of Darboux matrix, a new generalized Darboux transformations(DTs) for a(2 + 1)-dimensional nonlinear Schrdinger(NLS) equation is derived, which can be reduced to two(1 + 1)-dimensional equation:a modified KdV equation and an NLS equation. With the help of symbolic computation, some higher-order rational solutions and rogue wave(RW) solutions are constructed by its(1, N-1)-fold DTs according to determinants. From the dynamic behavior of these rogue waves discussed under some selected parameters, we find that the RWs and solitons are demonstrated some interesting structures including the triangle, pentagon, heptagon profiles, etc. Furthermore, we find that the wave structure can be changed from the higher-order RWs into higher-order rational solitons by modulating the main free parameter. These results may give an explanation and prediction for the corresponding dynamical phenomena in some physically relevant systems.     

Folded Localized Excitations in a Generalized (2+1)-Dimensional Perturbed Nonlinear SchrÖdinger System

Starting from a special Bäcklund transform and a variable separation approach, a quite general variable separation solution of the generalized (2+1)-dimensional perturbed nonlinear Schrödinger system is obtained. In addition to the single-valued localized coherent soliton excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.     

Bäcklund Transformat ion and Mult isoliton-Like Solutions for (2+1)-Dimensional Dispersive Long Wave Equations

A Bäcklund transformation of the (2+1)-dimensional dispersive long wave equations is derived by using the developed homogeneous balance method. by means of the Bäcklund transformation, the new multisoliton-like solution and other two types of exact solutions to these equations are constructed.     

Structures and stability of Ag clusters on Ag(1 1 1) and Ni(1 1 1) surfaces

The structures of the lowest total energy for small Ag_N clusters with N = 2-20, which are grown on Ag(1 1 1) and Ni(1 1 1) surfaces, have been determined using a combination of the embedded-atom method and the basin-hopping algorithm. It is found that the particularly stable Ag clusters with N<18 have similar geometries on both surfaces when comparing clusters of the same size. On the other hand, the geometries of the less stable Ag clusters in the same size range differ for the two surfaces. From N?18, the sizes of the particularly stable structures are different for the two different substrates. Due to the large size mismatch of the two types of atoms it is energetically unfavorable for Ag to form a pseudomorphic monolayer structures on Ni(1 1 1) and there is considerable strain produced at the interface. The effect of this strain and the increased adatom-substrate interactions lead to irregular and elongated structures of the adsorbed Ag clusters.     

Exact Solution to (1+1)-Dimensional Higher-Order Schrödinger Equation via an Extended Mapping Approach

Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrödinger equation (n=3,4) is solved. A new family of variable separation solutions with arbitrary functions is derived.     

Systematic study of α decay half-lives for even–even nuclei within a deformed two-potential approach

In this work, we systematically study the α decay half-lives of 196 even–even nuclei using a two-potential approach improved by considering nuclear deformation. The results show that the accuracy of this model has been improved after considering nuclear deformation. In addition, we extend this model to predict the α decay half-lives of Z = 118 and 120 isotopes by inputting the α decay energies extracted from the Weizsacker–Skyrme-type (WS-type) mass model, a simple nuclear mass formula, relativistic continuum Hartree–Bogoliubov theory and Duflo-Zuker-19 (DZ19) mass model. It is useful for identifying the new superheavy elements or isotopes for future experiments. Finally, the predicted α decay energies and half-lives of Z = 118 and 120 isotopes are analyzed, and the shell structure of superheavy nuclei is discussed. It shows that the shell effect is obvious at N = 184, while the shell effect at N = 178 depends on the nuclear mass model.     

Soliton molecules and mixed solutions of the(2+1)-dimensional bidirectional Sawada-Kotera equation

In this paper, we investigate some new interesting solution structures of the(2+1)-dimensional bidirectional Sawada–Kotera(bSK) equation. We obtain soliton molecules by introducing velocity resonance. On the basis of soliton molecules, asymmetric solitons are obtained by changing the distance between two solitons of molecules. Based on the N-soliton solutions,several novel types of mixed solutions are generated, which include the mixed breather-soliton molecule solution by the module resonance of the wave number and partial velocity resonance,the mixed lump-soliton molecule solution obtained by partial velocity resonance and partial long wave limits, and the mixed solutions composed of soliton molecules(asymmetric solitons), lump waves, and breather waves. Some plots are presented to clearly illustrate the dynamic features of these solutions.     

An Extended Subequation Rational Expansion Method and Solutions of (2+1)-Dimensional Cubic Nonlinear Schrödinger Equation

An extended subequation rational expansion method is presented and used to construct some exact analytical solutions of the (2+1)-dimensional cubic nonlinear Schrödinger equation. From our results, many known solutions of the (2+1)-dimensional cubic nonlinear Schrödinger equation can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. With computer simulation, the properties of new non-travelling wave and coefficient function's soliton-like solutions, and elliptic solutions are demonstrated by some plots.     

Resonance Y-type soliton solutions and some new types of hybrid solutions in the(2+1)-dimensional Sawada–Kotera equation

In this paper, based on N-soliton solutions, we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in (2+1)-dimensional integrable systems. Then, we take the (2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint. Next, by the long wave limit method, velocity resonance and module resonance, we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves, breather waves, high-order lump waves respectively. Finally, we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic.     

A(2+1)-dimensional nonlinear model for Rossby waves in stratified fluids and its solitary solution

In this paper,we investigate a(2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids.We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasigeostrophic potential vorticity equation with dissipation and topography under the generalized beta effect,and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method.Through the analysis of this model,it is found that the generalized beta effect and basic topography can induce nonlinear waves,and slowly varying topography is an external impact factor for Rossby waves.Additionally,the conservation laws for the mass and energy of solitary waves are analyzed.Eventually,the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method.Based on the solitary wave solutions obtained,we discuss the effects of dissipation and slowly varying topography on Rossby solitary waves.