Band 62, Heft 7-8

In this work, we extended the application of “the modified reductive perturbation method” to long water waves and obtained the governing equations of Korteweg - de Vries (KdV) hierarchy. Seeking localized travelling wave solutions to these evolution equations we have determined the scale parameter g 1 so as to remove the possible secularities that might occur. To indicate the effectiveness and the elegance of the present method, we studied the problem of the “dressed solitary wave method” and obtained exactly the same result. The present method seems to be fairly simple and practical as compared to the renormalization method and the multiple scale expansion method existing in the current literature

The analytical positons, negatons, and complexitons and their interaction solutions to the coupled Korteweg - de Vries (KdV) system are obtained via the Darboux transformation of the complex KdV equation. Furthermore, the preferences for the nonsingular solutions are discussed

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

By means of an extended tanh approach, new types of variable separated solutions u , v , w with two arbitrary lower-dimensional functions of the (2+1)-dimensional general Sasa-Satsuma (GSS) system are derived. Based on the derived variable separation excitation, abundant localized structures such as dromion, peakon and foldon are revealed by selecting appropriate functions p and q . Finally, some elastic and nonelastic interactions among special folded solitary waves are investigated both analytically and graphically. The explicit phase shifts for all the local excitations offered by the common formula are given and applied to these interactions in detail.

In this paper we investigate the generalized inhomogeneous higher-order nonlinear Schrödinger equations, generated recently by deforming the inhomogeneous Heisenberg ferromagnetic spin system through a space curve formalism [Phys. Lett. A 352, 64 (2006)] and construct their multisoliton solutions, using gauge transformation. The amplitude of the bright soliton solutions generated grows and decays with time, and there is an exchange of energy between soliton trains during interaction.

The Adomian decomposition method is implemented for solving a higher-order nonlinear Schrödinger equation in atmospheric dynamics. By means of Maple, the Adomian polynomials of an obtained series solution have been calculated. The results reported in this paper provide further evidence of the usefulness of Adomian decomposition for obtaining solutions of nonlinear problems.

This paper applies He’s parameter-expansion method to determine the limit cycle of oscillators in a u 3 / (1+ u 2 ) potential. The results are compared with the exact solutions. This shows that the method is a convenient and powerful mathematical tool for the search of limit cycles of nonlinear oscillators.

A hierarchy associated with the Li spectral problem is derived with the help of the zero curvature equation. It is shown that the hierarchy possesses bi-Hamiltonian structure and is integrable in the Liouville sense. Moreover, the mono- and binary-nonlinearization theory can be successfully applied in the spectral problem. Under the Bargmann symmetry constraints, Lax pairs and adjoint Lax pairs are nonlineared into finite-dimensional Hamiltonian systems (FDHS) in the Liouville sense. New involutive solutions for the Li hierarchy are obtained.

The dielectric constant (ε’) and dielectric loss (ε″) of dilute solutions of ethanol in benzene have been measured at 9.883 GHz at 25, 30, 35 and 40 °C using standard microwave techniques. The dielectric relaxation time (τ) and dipole moment (μ) at 25, 30, 35 and 40 °C have been calculated by using the single frequency concentration variation method suggested by Gopala Krishna. It is found that the dielectric relaxation process can be treated as a rate process like the viscous flow process. A monomer structure of C 2 H 5 OH in benzene solution has been inferred. Based upon these studies, the presence of solute-solvent associations has been proposed. The energy parameters for the dielectric relaxation process have been calculated and compared with the corresponding energy parameters of viscous flow.

The influence of overlap interactions between the bridging ligands and the metal d orbitals on the super-exchange coupling constant are studied by means of ab-initio restricted Hartree-Fock molecular orbital calculations. The interaction between the magnetic d orbitals and the HOMOs of the carboxylate oxygen atoms are investigated in homologous asymmetrically dibridged dicopper(II) complexes which have significantly different - 2 J values (the energy separation between the spin-triplet and spin-singlet states). In order to determine the nature of the fronter orbitals, extended Hückel molecular orbital (EHMO) calculations are also reported. The differences in the magnitude of the coupling constants and magnetic behaviour are rationalized in terms of the bridging ligand orbital complementary / countercomplementary concept.

The effect of ring substitution and N -chlorination on the molecular geometry of arylsulphonamides and N -chloro-arylsulphonamides have been studied by determining the crystal structures of 2-methyl- 4-chloro-benzenesulphonamide (2M4CBSA) and the sodium salt of N -chloro-2-methyl-4-chlorobenzenesulphonamide (NaNC2M4CBSA). The results are analyzed along with the crystal structures of benzenesulphonamide, 4-methyl-benzenesulphonamide and 4-chloro-benzenesulphonamide. The crystal structure of NaNC2M4CBSA has also been compared and correlated with the crystal structures of the above compounds and those of the sodium salts of N -chloro-benzenesulphonamide, N chloro- 4-methyl-benzenesulphonamide, N -chloro-4-chloro-benzenesulphonamide and N -chloro-2,4- dichloro-benzenesulphonamide. The crystal system, space group, formula units and lattice constants in Å of the new structures are: 2M4CBSA: triclinic, P 1, Z = 4, a = 7 . 9030(10), b = 8 . 6890(10), c = 13 . 272(2), α = 100 . 680(10)°, β = 98 . 500(10)°, γ = 90 . 050(10)°; NaNC2M4CBSA: monoclinic, C 2 /c , Z =4, a = 10 . 9690(10), b = 6 . 7384(6), c = 30 . 438(2), β = 98 . 442(7)°. The structure of 2M4CBSA is quite complex with four molecules in its asymmetric unit. The S-N bond length slightly decreases with substitution of electron-withdrawing groups, while the effect is more pronounced with disubstitution. The structure of NaNC2M4CBSA confirms that there is no interaction between nitrogen and sodium, and Na + is attached to one of the sulphonyl oxygen atoms. The Na + coordination sphere involves oxygen atoms from water moleculess of crystallization and neighbouring molecules. The S-N distance of 1.586 Å for the compound is consistent with a S-N double bond. The molecules are held together by hydrogen bonds with distances varying from 2.12 to 2.85 Å.

Graphite is widely used in technology because of its unique properties. A drawback of graphite is its low heat resistance in oxidizing atmospheres. To increase its heat resistance, Nb-Hf protective coatings were synthesized. Electrodeposition of niobium coatings on graphite with subsequent precise surface alloying of niobium with hafnium was studied. Electrochemical synthesis of Nb-Hf coatings from molten salt systems containing compounds of niobium and hafnium was used too. It was shown that Nb-Hf coatings with a planar growing front can be obtained if the concentration and therefore the limiting current density of the more electropositive component Nb is kept low. Nb-Hf coatings with a thickness of 20 - 30 μm have been obtained in this way from an NaCl-KCl-K 2 NbF 7 (1 wt%)-K 2 HfF 6 (10 wt%)-NaF (5 wt%) melt, above the limiting current density of niobium deposition.

The electrical conductivity of molten MCl-NdCl 3 (M = Li, Na, Rb and Cs) has been measured from the liquidus temperature up to ~ 1180 K. The measurements were performed in usual U-shaped capillary quartz cells with platinum electrodes. The molar conductivity (Λ) has been computed by using literature data on the densities of the binary systems. In all cases, when the temperature range exceeds about 100 K, the plot lnΛ vs. 1 /T is not a straight line. The activation energy of the conductivity does not remain constant but reduces with increasing temperature. In the specific and molar conductivity isotherms strong deviations from additivity are noted. The results are discussed in terms of octahedral local coordination of Nd 3+ over the entire concentration range.

The electrochemical cell: Se|TGSe single crystal |Se, with tri-glycine selenide as solid electrolyte was employed to observe the ferroelectric-paraelectric phase transition. The charge, which normally occurs on the surface of the ferroelectric crystal in the polar phase, is thus incorporated in the electrical double layer of the cell and can be precisely monitored. The pyroelectric currents can also be measured with this cell. The concentration changes on the surface of the single crystal after direct current polarization are observed.

The influence of bromide ions and temperature on the standard rate constants of the Eu(III)/Eu(II) redox reaction was determined. Cyclic voltammetry was used for the calculation of the kinetic parameters. It was shown that in NaCl-KCl (equimolar mixture)-NaBr (15 wt%)-EuCl 3 melts increase of the temperature from 973 K up to 1023 K leads to a drastical decrease of the standard rate constant k s for the Eu(III)/Eu(II) redox reaction. This unusual influence of the temperature on the k s value was explained by a change of the electron transfer mechanism. It is suggested that at 1023 K another mechanism becomes dominant - the transfer of electrons through dissolved bromine in the melt. Bromine appeared in the melt due to the decomposition of chloride-bromide or bromide complexes of Eu(III), and the concentration of bromine in the melt increased with the growth of temperature.

Magnetic measurements of molar susceptibilities as a function of temperature in the temperature range between 5 and 400 K were performed for the intermetallic compounds Hf 2 Co and HfCo 2 , using a SQUID magnetometer. The density of states at the Fermi level for Hf 2 Co was evaluated from the measured spin paramagnetic susceptibility. In addition, band structure calculations using the augmented plane waves plus local orbitals (APW+lo) method as implemented in the WIEN2k programme package for the two compounds were done. The obtained results were compared with the measured data.

Results of EPR and optical studies of VO 2+ doped in bis (glycine) cadmium(II) chloride, belonging to a third site as a substitutional one are reported. The spin Hamiltonian parameters obtained for the site are g zz = 1 . 9159, g yy = 1 . 9695, g xx = 1 . 9853, A zz = 210 . 4 G, A yy = 109 . 8 G, and A xx = 107 . 0 G. By correlating the EPR and spectral data, the molecular orbital bonding parameters have been evaluated.