Rogue wave solutions and rogue-breather solutions to the focusing nonlinear Schr?dinger equation

Based on the long wave limit method, the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schr?dinger equation are given by introducing some arbitrary parameters. The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions. By applying the same method to the three-breather solutions, two types of interaction solutions are obtained, namely the first-order...     

Existence,regularity, and asymptotic behavior of the solutions to the Ginzburg-Landau equations on ℝ3

This paper studies the solutions of the Ginzburg-Landau equations on ³ in the presence of an arbitrarily distributed external magnetic field. The existence and regularity of the solutions at the lowest energy level are established. The solutions found are in the Coulomb gauge. If the external field is sufficiently regular, the solutions are shown to have nice asymptotic decay properties at infinity.     

Resonances in 12C and Their Breakup to the 3α Final State

The breakup of ¹²C states into three -particles is discussed in the context of the continuum three-body problem. New information from the -decay of ¹²N populating 0⁺, 1⁺, and 2⁺ states in ¹²C is presented. The breakup mechanism of the 1⁺ state at 12.71MeV is clarified, the spin of the 10.3MeV state is determined as 0⁺, and evidence for a previously unknown 2⁺ state at 14.1(2)MeV is given.     

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.     

A class of solutions in the O(3) σ-model

In a recent paper Chelnokov and Zeitlin obtained a set of differential equations for the O(3) σ-model in euclidean space and solved it under some assumption. Similar equations were obtained by Popov and Zeitlin for a ³He film and solved it under another assumption. The present note generalises the solutions obtained by these two assumptions.     

Raman spectra and restructurizations in the system of solid solutions NaTa y Nb1−y O3

By recording the Raman spectra, concentrational restructurizations in the system of solid solutions NaTa_yNb_1−yO₃ were investigated. The regions of relatively stable existence of solid solutions (y<0.2, y>0.8) and the region of a rather high disordering (0.2<y<0.9) with maximum deformation of the elementary cell at y=0.5 have been revealed. It is found that at y=0.5 a concentrational phase transition is observed, and at y ∼ 0.25 and 0.8 concentrational restructurizations occur. It is shown that the octahedral anions of BO₆ are centrosymmetric when y<0.2 and y>0.9, and the system of solid solutions NaTa_yNb_1−yO₃ is antiferroelectric when y<0.2. In the range of concentrations 0.2<y< 0.9, the structure of NaTa_yNb_1−yO₃ is characterized by the presence of polar clusters. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 2, pp. 192–198, March–April, 2000.     

Exact periodic wave solutions to the coupled Schrödinger-KdV equation and DS equations

The exact solutions for the coupled non-linear partial differential equations are studied by means of the mapping method proposed recently by the author. Taking the coupled Schrödinger-KdV equation and DS equations as examples, abundant periodic wave solutions in terms of Jacobi elliptic functions are obtained. Under the limit conditions, soliton wave solutions are given.     

Multivalued solutions of the φ4-field equations,transition to ergodicity and bifurcations

The polynomial nonlinear Klein-Gordon equation analyzed in this paper is an Euler equation for the classical “φ⁴”-field theory in euclidean space. It is of great importance in a variety of condensed matter applications, especially for critical systems. The symmetry reduction for partial differential equations has been used here to find a number of exact solutions of this equation. These solutions have an interesting property of multi-valuedness. In particular, for some values of the parameters of the theory these solutions exhibit transition to ergodicity. A brief discussion of the physical significance of these results is also given.     

Electronic structure and optical spectra of YBa2Cu3O7−δ thin films in the infrared and UV region

Optical reflectance of YBa₂Cu₃O_7- thin films grown by laser ablation is measured within photon energies of 0.1 eV to 3.5 eV at room temperature. The spectra can be fit congruently with the anisotropic dielectric constants which take account of the intraband free carrier transition and interband transition. The anisotropic plasma frequencies are simulated to be _pl=2.18 eV and _ch=2.80 eV contributed from free carriers on the plane and in the chain, respectively. The interband transition occurs near 2.5 eV and is pertinent to a rather broad line width.     

Concentration-dependent structural transition in the La0.70Sr0.30MnO3−δ system

The crystal structure of anion-deficient La_0.70Sr_0.30MnO_3?δ manganites (δ = 0, 0.10, 0.15, and 0.20) has been studied by powder neutron diffraction at room temperature. The crystal structures of the stoichiometric La_0.70Sr_0.30MnO₃ and anion-deficient La_0.70Sr_0.30MnO_2.90 samples are satisfactorily described by the rhombohedral R $\bar 3$ c space group. The anion-deficient La_0.70Sr_0.30MnO_2.85 sample separates into two perovskite phases with the R $\bar 3$ c and I4/mcm space groups. The crystal structure of La_0.70Sr_0.30MnO_2.80 cannot be described by a single perovskite phase in the I4/mcm space group. It is found that the clustering of oxygen vacancies is the cause of structural phase separation at 293 K in anion-deficient La_0.70Sr_0.30MnO_3?δ manganites.     

Correlation between the “fishtail” effect in the magnetization and the Schottky contribution in the specific heat of high purity YBA2Cu3O7−δ crystals

The irreversibility of the magnetization and the low temperature specific heat of high purity YBa₂Cu₃O_7– crystals are investigated. We find that the heat treatment that suppresses the magnetic fishtail effect also suppresses the Schottky component of the heat capacity. Both effects originate from the distribution of oxygen states.     

Diffusion coefficients of sodium dodecylsulfate in aqueous solutions and in aqueous solutions of β-cyclodextrin

Differential diffusion coefficients have been measured of sodium dodecylsulfate (SDS) in aqueous solutions of β-cyclodextrin (β-CD) at 298.15 K over the concentration range 0.001 M to 0.0817 M using a conductimetric cell and an automatic apparatus to follow the diffusion. The cell uses an open ended capillary method, while a conductimetric technique is used to follow the diffusion process by measuring the resistance of a solution inside the capillaries, at various recorded times. The β-CD is known to for strong 1:1 complexes with SDS, and the effect of this on the diffusion of this electrolyte was investigated. The presence of β-cyclodextrin can influence the diffusion coefficients of sodium dodecylsulfate both above and below the critical micelle concentration (cmc) of this surfactant. For concentrations of β-cyclodextrin of 0.001 mol dm⁻³ the behaviour of the diffusion of SDS in aqueous solutions is the same in the absence or the presence of β-cyclodextrin. In contrast, when the β-CD concentration is 0.016 mol dm⁻³ we obtain diffusion coefficients higher than those obtained in aqueous solutions. Further, we do not observe the dramatic decrease in diffusion normally found at the cmc of the surfactant. These results are interpreted in terms of the effect of incorporation of dodecylsulfate chains inside the cyclodextrin cavities.     

Total conductivity in Sc-doped LaTiO3 + δ perovskites

A series of Sc-doped lanthanum titanate perovskites, LaTi_(1???x)Sc _x O_3?+?δ with x?=?0, 0.2, 0.25 and 0.3, was prepared by sol-gel method. All compositions were found to exhibit orthorhombic crystal structure. An increase in unit cell volume was observed for composition with x?=?0.2. The oxidation states of La³⁺, Sc³⁺ and Ti³⁺ ions have been established using X-ray photoelectron spectroscopy (XPS). It is observed that an enhancement in total conductivity of LaTiO_3?+?δ perovskite is achieved only at lower doping concentration. A reverse effect is observed for higher dopant concentration.     

Oxygen thermodynamics and ion conductivity in the solid solution La1−xSrxCoO3−δ at large strontium content

The equilibrium oxygen content was measured in the model system and important oxygen permeable material La_1−xSr_xCoO_3−δ, where x=0.6, in the temperature range 650–900 °C and oxygen partial pressure range between 10⁻⁵ and 1 atm. The data were utilized to obtain changes in the partial entropy and enthalpy of oxygen in the solid as a function of the oxygen content. It is shown that the initially cubic perovskite undergoes to a phase transition to a tetragonal structure at δ >0.3. The oxygen permeation of L_0.4Sr_0.6CoO_3−δ at 700–900 °C is found to be controlled by bulk solid state processes. The activation energy equals about 0.8 eV at high oxygen pressure and small oxygen nonstoichiometry. Increasing oxygen deficiency results in a rapid increase in the activation energy. In combination with thermodynamic data, these changes can be explained as resulting from the intrinsic spatial inhomogeneouty in oxygen vacancy distribution which varies both with temperature and oxygen nonstoichiometry. It is shown that, when the oxygen deficiency increases at constant temperature, the oxygen vacancies form locally ordered microdomains (clusters), which eventually results in a transition of the cubic perovskite structure to the tetragonal structure. The oxygen ion conductivity depends strongly on the development of the ordering. Paper presented at the 6th Euroconference on Solid state Ionics, Cetraro, Calabria, Italy, Sept. 12–19, 1999.     

Study of the glassy magnetic behaviour and charge-ordering phase transitions in La0.75Ca0.25FeO3−δ perovskite

Abstract

In this work, La_0.75Ca_0.25FeO_3?δ perovskite sample was prepared by the coprecipitation method. The nanoparticle was found to crystallize in the orthorhombic (Pbnm) phase as confirmed by X-ray diffraction (XRD) and transmission electron microscopic (TEM). The oxygen non-stoichiometry (δ) and magnetic states of iron ions (three magnetic sextets and non-magnetic doublet) were investigated by Mössbauer spectroscopy at room temperature (RT). The shape of the magnetic hysteresis loop of the sample reveals the existence of a weak ferromagnetism at RT. The magnetization vs. temperature curves, measured in the 9 to 200 K range, showed that the sample exhibits two magnetic-phase transition temperatures at 29 K (T_g) and 120 K (T_CO). The magnetization isotherms, M (H), around these magnetic-phase transition temperatures for the sample are analyzed.     

Soliton and shock wave solutions to the Degasperis–Procesi equation with power law nonlinearity

This paper obtains the solitary wave as well as the shock wave solutions of the Degasperis–Procesi equation. Both regular nonlinearity as well as power law nonlinearity are considered. The constraint relations are identified in the process of obtaining the nonlinear wave solutions.