Volume 60, Issue 4

In this paper, a new generalized algebraic method is proposed to construct a series of explicit exact solutions of general nonlinear evolution equations with variable coefficients. Compared with most existing methods, such as the tanh method, the extended tanh method, the Jacobi elliptic function method or the algebraic method, the proposed method seems to be more powerful. The efficiency of the method is demonstrated by applying it to the (1+1)-dimensional variable coefficients modified Korteweg-de Vries (MKdV) equation and the (2+1)-dimensional variable coefficients Kadomtsev- Petviashvili (KP) equation. A rich variety of new exact explicit solutions has been found. - PACS numbers: 03.40.Kf; 03.65.Fd; 02.30Jr.

In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2+1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the Jacobi elliptic function, soliton-like trigonometric function solutions, and so on. Our method can be applied to other nonlinear evolution equations.

Applying a symmetry group theorem on a two-straight-line soliton, some types of new localized multiply curved line excitations including the plateau-basin type ring solitons are obtained.

The Jacobi elliptic function solutions of coupled nonlinear partial differential equations, including the coupled modified KdV (mKdV) equations, long-short-wave interaction system and the Davey- Stewartson (DS) equations, are obtained by using the mixed dn-sn method. The solutions obtained in this paper include the single and the combined Jacobi elliptic function solutions. In the limiting case, the solitary wave solutions of the systems are also given. - PACS: 02.30.Jr; 03.40.Kf; 03.65.Fd

In this work, a novel phenomenon that localized coherent structures of a (2+1)-dimensional physical model possess fractal properties is discussed. To clarify this interesting phenomenon, we take the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) system as a concrete example. First, with the help of an extended mapping approach, a new type of variable separation solution with two arbitrary functions is derived. Based on the derived solitary wave excitation, we reveal some special regular fractal and stochastic fractal solitons in the (2+1)-dimensional BLP system. - PACS: 05.45.Yv, 03.65.Ge

We consider nonlinear dynamical systems with chaotic and hyperchaotic behaviour.We investigate the behaviour of the Hurst exponent at the transition from chaos to hyperchaos. A two-dimensional coupled logistic map is studied.

The anomalous acceleration of spacecrafts in the solar system is explained. An explanation of the observed superluminal velocities of jets at extragalactic objects is given. The extension of quasars can be larger as generally assumed, i. e. quasars must not be very compact objects. An explanation of the high energy loss per unit time of quasars is given. The relation between the velocity of an object in the universe and its redshift is stated. All these results are received from cosmological models studied by flat space-time theory of gravitation and the post-Newtonian approximation of perfect fluid in these cosmological models where clocks at earlier times are going faster than at present.

Optimized geometrical parameters, electron densities, heats of formation and stabilization energies have been obtained on X-substituted phenylallyl alcohols, where X is H, OCH 3 , NH 2 , CN, F and CH 3 at ortho, meta, and para positions, using MINDO-Forces SCF-molecular orbital calculations. The substituent effects on the geometrical parameters and the electron density are discussed.

The local structure of the tetragonal Er 3+ center in CaO is theoretically studied by using the perturbation formulas of the g factors for a 4f 11 ion in tetragonal symmetry. In these formulas, the contributions to the g factors from the second-order perturbation terms and the admixtures of various states are taken into account. Based on the investigations, this center is suggested to be the impurity Er 3+ substituting the host Ca 2+ site, associated with a Ca 2+ vacancy V Ca in the [100] (C 4 ) axis due to charge compensation. By studying the g factors of the tetragonal center, impurity Er 3+ is expected to undergo an off-center displacement ΔZ(≈ 0.2 Å ) towards the V Ca along the C 4 axis because of the electrostatic attraction. The calculated g factors based on the displacement ΔZ show reasonable agreement with the observed values.

Dust acoustic solitary waves are investigated on the nonlinear, unmagnetized homogeneous dust ion and dust ion electron plasma with the effects of dust streaming. The Sagdeev’s pseudopotential is determined in terms of u d , the dust ion speed. It is found that there exist a critical value of u d , beyond which the solitary waves cease to exist.

Stark width (W) and shift (d) of the neutral helium (He I) 402.6186 nm spectral line in the high lying 2p-5d transition have been measured in the optically thin helium plasma created in a linear, low-pressure, pulsed arc discharge at a 52,000 K electron temperature and 1.3 · 10 23 m −3 electron density. Obtained data are the first experimental values of the Stark width and shift related to the mentioned He I spectral line. Direct comparison with theoretical results is not possible due to the fact that available data are calculated for considerably lower electron densities. We found that at 10 23 m −3 electron density the lowering of the effective ionization energy has influence on the number and contribution of the perturbing energy levels, especially in the case of the high lying parent energy level of the particular transition. This effect generates lower Stark widths in the high lying He I transitions than the existing theoretical approximations provide. We have found negative Stark shift.

Complexes of M(benzoic acid) 2 Ni(CN) 4 (M = Ni, Cd, Co and Mn) are obtained for the first time. The observed spectra indicate that the obtained complexes are new examples of Hofmann-type complexes. -PACS NO: 33.20.Ea, 33.20.Tp

Six solid phases of [Mn(DMSO) 6 ](ClO 4 ) 2 have been detected by differential scanning calorimetry. The phase transitions were found between the following solid phases: stable KIc ↔ stable KIb at T C5 = 225 K, metastable KIII ↔ metastable KII at T C4 = 322 K, stable KIb ↔ stable KIa at T C3 = 365 K, metastable KII↔overcooled K0 at T C2 = 376 K and stable KIa→stable K0 at T C1 = 379 K. The title compound melts at T m = 488 K.

Density studies on the isotropic to smectic-F transition in higher homologues of N-(p-nalkoxybenzylidene)- p-n-decylanilines ( n O.10) mesomorphic compounds with n = 13, 14 and 15 and corresponding studies on thermal expansion coefficient maxima confirm the first order nature of this transition. The density shows strong pretransitional fluctuations, which are estimated by α eff in the vicinity of the mesomorphic fluctuation dominated non-linear region (FDNLR) of this phase transition. The growth of the density fluctuations across this transition is discussed in the light of data on the same transition in other compounds.