Volume 60, Issue 5

In this paper, two transformations are introduced to solve the double sine-Gordon equation by using knowledge of the elliptic equation and Jacobian elliptic functions. It is shown that different transformations can be applied to obtain more kinds of solutions to the double sine-Gordon equation. PACS: 03.65.Ge

The generalized coupled Korteweg-de Vries (GCKdV) equations as one case of the four-reduction of the Kadomtsev-Petviashvili (KP) hierarchy are studied in details. The Painlevé properties of the model are proved by using the standard Weiss-Tabor-Carnevale (WTC) method, invariant, and perturbative Painlev´e approaches. The meaning of the negative index k = −2 is shown, which is indistinguishable from the index k = −1. Using the standard and nonstandard Painlevé truncation methods and the Jacobi elliptic function expansion approach, some types of new exact solutions are obtained.

Exact periodic wave solutions in terms of the Jacobi elliptic functions are obtained to the Melnikov equation by means of the extended mapping method with symbolic computation. The stability of these periodic waves is numerically studied. The results show that the linearly combined waves of cn− and dn− functions can propagate stably. For the blow up solutions, the linearly combined periodic solutions of nd− and sd− functions and of dc− and sc− functions can also propagate stably and others can not do. Under the limit conditions, some new solitary wave solutions and trigonometric periodic wave solutions are got. The method is applicable to a large variety of nonlinear partial differential equations. - PACS: 05.45.Yv, 02.30.Ik, 02.30.Jr

The generation of lump solitons by a three-dimensional bottom topography is numerically investigated by use of a forced Kadomtsev-Petviashvili-I (KP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the pairwise periodic generation of two pairs of lump-type solitons downstream of the obstacle. The pair with the smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with the larger amplitude. Furthermore, the effects of the detuning parameter on the generation and evolution of lumps are studied. Finally the waves propagating upstream of the obstacle are also briefly investigated.

We propose a two-dimensional model for a co-evolving ecosystem that generalizes the extremal coupled map lattice model. The model takes into account the concept of multiobjective optimization. We find that the system is self-organized into a critical state. The distribution of avalanche sizes follows a power law.

For a class of Bardeen-Cooper-Schrieffer (BCS)-models, with complex, weakly momentum dependent interaction coefficients, the representation dependent effective Hamiltonians and their spectra are reconsidered in order to obtain a consistent physical picture by means of operator algebraic methods. The starting point is the limiting dynamics, the existence of which had been proved in a previous work, in terms of a C*-dynamical system acting in a classically extended, electronic Canonical Anticommutation Relations (CAR)-algebra. The C*-algebraic KMS-theory, including the low temperature limit, specifies the order parameters. These appear as classical observables, which commute with all other observables, constituting elements of the center of the algebra. The algebraic spectral theory, in the sense of Arveson, is first applied to the dynamics in general pure energy state representations. The spectra of the finite temperature representations are analyzed, identifying the gap as the lowest of those energy values, which are stable under local perturbations. Further insights are obtained by decomposing the thermal dynamical systems into the pure energy state Heisenberg dynamics, after having first extended them to more comprehensive W*-dynamical systems. The decomposing orthogonal measure is transferred to the infinite product space of quasi-particle occupation numbers and its support is characterized in terms of 0-1-laws leading to an asymptotic ratio of quasi-particles and holes, which depends on the temperature. This ratio is connected with an algebraic invariant of the representation dependent observable algebra. Energy renormalization aspects and pair occupation probabilities are discussed. The latter reveal, beside other things, the difference between macroscopic term occupation and coherent macroscopic term occupation for a condensate.

The g factors of Fe + in MgO and CaO are theoretically investigated by the perturbation formula of the g factor of a 3d 7 ion in cubic octahedral symmetry based on the cluster approach. By considering the partial quenching of the spin-orbit coupling interaction and the effective Land´e factor due to the dynamic Jahn-Teller effect (DJTE), the experimental g factors of the studied systems are reasonably interpreted. It can be suggested that the small g factors of the Fe + centers in MgO and CaO can be likely attributed to the DJTE, rather than the covalency effect within the scheme of the static crystalfield model.

The EPR g factors of Cr 3+ in NaCrS 2 and NaCrSe 2 crystals are calculated from the high-order perturbation formulas based on the one-spin-orbit (SO)-coupling-parameter (i. e., the SO-couplingparameter of the central 3d n ion) as well as the two-SO-coupling-parameter (i. e., the SO-couplingparameter of the 3d n ion and that of ligands) models for 3d n ions in cubic octahedral sites. The calculated results (in particular for NaCrSe 2 ) based on the two-SO-coupling-parameter model are closer to the observed values than those based on the one-SO-coupling-parameter model, suggesting that for calculations of the g factor of 3d n ions in covalent crystals the two-SO-coupling-parameter model is preferable to the one-SO-coupling-parameter model. The reasonableness of the calculated results from the two-SO-coupling-parameter model is discussed.

The electron paramagnetic resonance (EPR) anisotropic g-factors g x , g y and g z and hyperfine structure constants A x , A y and A z of Cu 2+ in Cs 2 ZnCl 4 crystal are theoretically investigated by the method of diagonalizing the full Hamiltonian matrix. The crystal-field parameters are obtained from the crystal structure by the superposition model. The results, agreeing reasonably with the observed values, are discussed.

N-(2,4-Dichloro)-salicylaldimine was synthesized, characterized by elemental analysis, FT-IR, and UV-visible spectroscopy, and its crystal structure was determined. The title compound is almost planar and contains short intramolecular O-H. . .N hydrogen bonds [O1-N1 2.601(1) A° ]. It remains transparent in the visible region and has solvatochromic behavior in the UV region in the range 198 - 349 nm, implying non-zero microscopic first hyperpolarizability. The ab-initio quantum mechanical calculations (finite field second-order Møller Plesset perturbation theory) of the studied compound have been carried out to compute the electric dipole moment (μ) and the first hyperpolarizability (β ) values. The ab-initio results also show that this ligand might have microscopic nonlinear optical behavior with non-zero values.