Volume 62, Issue 1-2

With the help of the symbolic computation system Maple and an expanded projective Riccati equation approach, we obtain some new rational explicit solutions with three arbitrary functions for the (2+1)-dimensional Boiti-Leon-Pempinelli system, including Weierstrass function solutions, solitary wave solutions and trigonometric function solutions. From these, several y-periodic soliton localized excitations are constructed and some evolution properties of these novel y-periodic localized structures are discussed.

By means of an improved mapping approach, a series of excitations of the (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific fission, fusion and annihilation phenomena of solitons are also obtained. - PACS numbers: 05.45.Yv, 03.65.Ge.

In this paper, the physically interesting variable-coefficient higher-order nonlinear Schr¨odinger models in nonlinear optical fibers with varying higher-order effects such as third-order dispersion, self-steepening, delayed nonlinear response and gain or absorption are investigated. The bilinear transformation method is modified for constructing the analytic solutions of these models directly with sets of parametric conditions. With the aid of symbolic computation, the explicit analytic multisolitonic solutions of the variable-coefficient higher-order nonlinear Schr¨odinger models are presented by employing the modified bilinear transformation method. The one- and two-solitonic solutions in explicit form are given in detail. Finally, solutions are illustrated and discussed through adjusting the parameters, so different dispersion management systems can be obtained.

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k 3 ), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.

A function projective synchronization is defined to synchronize two different systems up to a scaling function matrix f with different initial values. The function projective synchronization is more general than the complete synchronization, the generalized projective synchronization and the modified projective synchronization. The corresponding framework of synchronization is set up and used to achieve a function projective synchronization design of two different chaotic systems: the unified chaotic system and the Rössler system. Feasibility of the proposed control scheme is illustrated through the numerical simulation.

The propagator of two-dimensional Dirac oscillator in the presence of a constant magnetic field is presented by means of path integrals, where the spin degree-of-freedom is described by odd Grassmannian variables and the gauge invariant part of the effective action has the form of the standard pseudoclassical action given by Berezin and Marinov. Then the path integration is carried out and the problem is solved exactly. The energy spectrum of the electron and the wave functions are extracted. - PACS numbers: 03.65.Ca, 03.65.Db, 03.65.Pm, 03.65.Ge.

The behaviour of a system composed of malonic acid (MA), KBrO 3 , H 2 SO 4 , and ferroin was investigated in batch experiments at various concentrations of oxygen above the chemical mixture when changing the concentration of MA. We could observe that at 10% of oxygen or more and for initial concentrations of malonic acid [MA] 0 between 0.15 M and 0.6 M the system attains an equilibrium by some of mixed mode oscillations. Such a behaviour of the system could be described by a model used lately. Additionally for [MA]0 = 0.1 M or less at 0 - 20% of oxygen a region of sequential oscillations was discovered (observed for the first time in the system with ferroin) and a trial of understanding of the event is suggested. For rather small [MA] 0 ca. 0.025 M no mixed mode oscillations, no sequential ones but the so-called relaxation oscillations were observed.

A computational study at the level of density functional theory (DFT) was carried out to investigate the influence of carbon doping (C-doping) on the 11 B and 14 N quadrupole coupling constants (CQ) in the (6,0) single-walled boron-nitride nanotube (BNNT). To this aim, a 10 Å length of BNNT consisting of 24 B atoms and 24 N atoms was selected where the end atoms are capped by hydrogen atoms. To follow the purpose, six C atoms were doped instead of three B and three N atoms as a central ring in the surface of the C-doped BNNT. The calculated CQ values for both optimized BNNT systems, raw and C-doped, reveal different electrostatic environments in the mentioned systems. It was also demonstrated that the end nuclei have the largest C Q values in both considered BNNT systems.

The dielectric properties of n-nonyloxycyanobiphenyl in the isotropic (I), nematic (N) and smectic A (S A ) phases were investigated. The dielectric relaxation spectra, recorded in the frequency range 50 kHz - 100 MHz, were analyzed with use of the Cole-Cole equation. An anomalous temperature behavior of the static permittivity, the rotational diffusion exponent and the activation energy of mesogenic molecules rotating around their short axis, observed in the vicinity of the phase transitions, are discussed.

Six solid phases of [Ni(DMSO) 6 ](ClO 4 ) 2 have been detected by differential scanning calorimetry (DSC). The five phase transitions were detected between the following solid phases: metastable KIII ↔ undercooled K0 at T C5 = 326 K, stable KIb → stable KIa at T C4 = 350 K, metastable KII ↔ undercooled KI at T C3 = 353 K, stable KIa → stable KI at T C2 = 365 K and stable KI → stable K0 at T C1 = 380 K. At T m2 = 459 K the title compound partially dissolves in DMSO, which arises from the decomposition of [Ni(DMSO) 6 ](ClO 4 ) 2 to [Ni(DMSO) 5 ](ClO 4 ) 2 , and at T m1 = 526 K created in this way a substance which completely melts. From the entropy changes at the melting point and at phase transitions it can be concluded that the phases K0 and undercooled K0 are orientationally dynamically disordered crystals. The stable phases KI, KIa, KIb and the metastable phases KII and KIII are more or less ordered solids.

Dilatometric studies are carried out on liquid crystals (LCs), viz., p-(phenyl benzylidene)-p 1 - alkylanilines (PBnA for n = 7 - 10, 12, 14 and 16). LC PBnA compounds are found to exhibit four different types of phase variants. The lower homologues (for n = 3 - 6) exhibit an NBE trivariant, intermediate homologues (with n = 7 - 9) exhibit an NABE tetravariant, higher homologues (for n = 10 - 12) exhibit an ABE tetravariant, and long higher homologues (for n = 14 and 16) exhibit an AB bivariant phase sequence. Dilatometry studies in PBnA compounds infer the first order nature for IN (for n = 7, 8 and 9), IA (for n = 10, 12, 14 and 16), NA (for n = 8 and 9) and AB (for n = 14 and 16) phase transitions. Phase transitions involving the growth of the 3D smectic-B phase in PBnAs are found to be tuned by squeezing of orientational disorder. A comparative study of phase transitions exhibited by PBnA compounds is presented along with the data in other Schiff base compounds.

70 N-( j,k-Dichlorophenyl / j,k-dimethylphenyl)-acetamides and substituted acetamides of the general formula j,k-X′ 2 C 6 H 3 NH-CO-CH 3 − i X i ( j,k = 2,3; 2,4; 2,5; 3,4 or 3,5; X, X′ = Cl or CH 3 ; i = 0, 1, 2 or 3) have been synthesized and their 1 H and 13 C NMR spectra in solution were studied. The influence of Cl and methyl substitution in the side chain as well as in the aryl group was ystematically investigated and discussed in detail. Chemical shifts of all aromatic protons and carbon atoms were computed by adding the substituent contributions in three different ways to those of the unsubstituted molecules. The agreement with the experimental values is discussed in detail for the three different methods of calculation.

The crystal structures of N-(meta-substituted phenyl)-2,2,2-trichloro-acetamides such as N- (3-methylphenyl)-2,2,2-trichloro-acetamide, 3-CH 3 C 6 H 4 NH-CO-CCl 3 (3MPTCA); N-(3-chlorophenyl)- 2,2,2-trichloro-acetamide, 3-ClC 6 H 4 NH-CO-CCl 3 (3CPTCA); N-(3,5-dimethylphenyl)- 2,2,2-trichloro-acetamide, 3,5-(CH 3 ) 2 C 6 H 3 NH-CO-CCl 3 (35DMPTCA) and N-(3,5-dichlorophenyl)- 2,2,2-trichloro-acetamide, 3,5-Cl 2 C 6 H 3 NH-CO-CCl 3 (35DCPTCA) have been determined at room temperature. The crystal system, space group, formula units and lattice constants (Å ) of the new structures are: 3MPTCA: orthorhombic, Pbca, Z = 8, a = 12.3199(11), b = 8.9719(8), c = 20.2058(15); 3CPTCA: orthorhombic, Fdd2, Z =16, a=19.285(4), b=40.765(8), c=5.5920(11); 35DMPTCA: triclinic, P1̄, Z = 2, a = 8.994(4), b = 9.9890(10), c = 14.760(5), α = 79.56(2)°, β = 73.32(3)°, γ = 86.47(2)°; and 35DCPTCA: orthorhombic, Pbca, Z = 8, a = 22.485(5), b=10.738(2), c=10.028(3). The compound 35DMPTCA has two molecules in its asymmetric unit, similar to o-NO 2 -, m-NO 2 - and p-CH 3 -substituted phenyl-trichloro-acetamides, while 3MPTCA, 3CPTCA and 35DCPTCA have one molecule each in their asymmetric units. The analysis of data indicates that the substitution of a strong electron withdrawing group such as a nitro group into PTCA at ortho or meta positions has a significant effect on the crystal parameters.

The EPR zero-field splittings of Fe 3+ doped in MgTiO 3 and LiTaO 3 are studied by diagonalizing the complete energy matrices of the electron-electron repulsion, ligand-field and spin-orbit coupling interactions for a d 5 configuration ion in a trigonal ligand-field. It is shown that, when Fe 3+ is doped in aMgTiO 3 or LiTaO 3 crystal, the local lattice structure around the octahedral Fe 3+ center has an obvious distortion along the C 3 axis. By simulating the second- and fourth-order EPR parameters D and (a−F) simultaneously, the local structure parameters of Fe 3+ doped inMgTiO 3 and LiTaO 3 crystals are determined, which reveal that Fe 3+ occupies both the Mg 2+ and Ti 4+ sites in the MgTiO 3 :Fe 3+ system and occupies the Li + site rather than the Ta 5+ site in the LiTaO 3 :Fe 3+ system. The results accord with the ENDOR and EPR experiments. - PACS numbers: 71.70.Gm; 75.30.Et; 71.70.Ch.