Solitonic waves in polyene dications and principles of charge carrier localization in π‐conjugated organic materials

The quantum‐chemical investigations by ab initio method (restricted Hartree–Fock/6‐31G**) have been performed for a series of unsubstituted, monosubstituted, and disubstituted neutral polyenes and their double charged cations. The waves of charge alternation (characterized by the difference in the electron densities at the nearest carbon atoms or Δq function) and bond length alternation (characterized by the lengths difference of the nearest carbon–carbon bonds or Δl function) are reported. Comparisons are made with the corresponding monocationic polymethine molecules. We found that ionization by two electrons results in formation of two solitonic waves of charge alternation, rather than superposition of two overlapping solitonic waves into one. These waves behave similar to two independent elastic particles, which do not penetrate into each other despite the special confinement by the length of chromophore π‐system. In monosubstituted polyene dication, Δq and Δl functions contain two waves each; however, only one wave is mobile and sensitive to a change of the chemical nature of the terminal group, whereas the second wave remains practically unchanged. The introduction of one oxymethyl or phenyl terminal groups leads to a relatively small shift of the mobile wave from the center to a direction of the terminal group. The effect of the amino or tropilium terminal groups is much more pronounced and leads to a shift of the mobile wave to the end of the molecule. In disubstituted polyene dication, both solitonic waves become mobile and shift symmetrically to both ends. The general principles of the charge localization described in this study may be used in molecular design and fine‐tuning of the charge transport properties in plastic photovoltaics and other organic semiconducting materials. © 2012 Wiley Periodicals, Inc.     

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

Solitonic Information Transmission in General Relativity

An exact solution of the vacuum Einstein＇s field equations is presented, in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation. On the basis of this exact solution, the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.     

Painlevé test for integrability for a combination of Yang’s self-dual equations for <Emphasis Type="Italic">SU</Emphasis> (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics and a comparative discussion among the three

Painlevé test for integrability for the combined equations generated from Yang’s self-dual equations for SU (2) gauge fields and Charap’s equations for chiral invariant model of pion dynamics faces some peculiar situations that allow none of the stages (leading order analysis, resonance calculation and checking of the existence of the requisite number of arbitrary functions) to be conclusive. It is also revealed from a comparative study with the previous results that the existence of abnormal behaviour at any of the stated stages may have a correlation with the existence of chaotic property or some other properties that do not correspond to solitonic behaviour.      

Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas

Plasmas are believed to be possibly the most abundant form of ordinary matter in the Universe, supporting a variety of the wave phenomena, while a dusty plasma is of interest as a non-Hamiltonian system of interacting particles. In this Letter, symbolic computation on an observationally/experimentally-supported (2+1)-dimensional generalized variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation is done, for certain dust-acoustic, electron-acoustic, positron-acoustic, magneto-acoustic, dust-magneto-acoustic, ion-acoustic, dust-ion-acoustic and/or quantum-dust-ion-acoustic waves in one of the cosmic/laboratory dusty plasmas. Auto-Bäcklund transformation and families of the solitonic solutions are obtained, for the electrostatic wave potential, perturbation of the magnitude of the magnetic field, fluctuation of electron or ion density, or radial-direction component of the velocity of ions or dust particles, relying on such plasma coefficient functions as the nonlinearity, dispersion, dusty-fluid-viscosity/Burgers-dissipation, geometric-effect and diffraction/transverse-perturbation coefficients. Shock structures presented in this Letter are very close to the experimental results previously reported. Future plasma observations/experiments might verify some other effects offered by our analytic results with respect to those plasma coefficient functions.     

Activation by nonlinear oscillations and solitonic excitations

Local excitations in molecular systems are studied taking into account the influence of soft impurities. The dynamics of activation processes (high-energy events) due to nonlinear mechanisms is studied. The following examples of classical macroscopic systems with strong nonlinear interaction are investigated: 1D Toda chains, 1D Morse rings, and 3D systems of hard spheres including impurities. It is shown that solitonlike excitations may lead to the concentration of energy at definite sites (weak springs or soft spheres). The accumulation of energy is mainly due to soliton-fusion effects. In thermal equilibrium an optimum temperature exists, where the thermally averaged potential energy is preferably partitioned to the soft springs embedded into a hard-spring solvent. Further, we show that the effect of thermal energy localization and the temperature dependence also persists for solutions of soft spheres in hard-sphere solvents.     

Bäcklund transformation and conservation laws for the variable-coefficient <Emphasis Type="Italic">N</Emphasis>-coupled nonlinear Schrödinger equations with symbolic computation

Considering the integrable properties for the coupled equations, the variable-coefficient Ncoupled nonlinear Schrödinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bäcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.     

Symbolic Computation of Extended Jacobian Elliptic Function Algorithm for Nonlinear Differential-Different Equations

The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schr ödinger equation. When the modulous m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.     

Bilinear forms through the binary Bell polynomials,N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach

Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-Bäcklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and Bäcklund transformations are different from those in the existing literature. All of our results are dependent on the water-wave dispersive power.     

High Conductivity Mediated by Thermal Excitation of Solectrons

We study the quantum dynamics and statistics of electrons interacting with nonlinear excitations of a classical thermal lattice of atoms on a semi‐phenomenological basis. By theoretical estimates based on tight‐binding approximations, Wigner distributions and computer simulations we show the existence of fast and nearly loss‐free motions of electrons along crystallographic axes of a nonlinear lattice. Using mass‐action relations we estimate the density of moving bound states between electrons and lattice solitons and estimate analytically and by simulations Wigner momentum distributions which are non‐Maxwellian. Calculating the currents from these bimodal distributions we show that thermally excited solectrons in nonlinear media may lead to a considerable transport enhancement. Our estimates and simulations demonstrate that in a temperature window, where solectrons are excited and are relatively stable, conductivity and diffusion may be enhanced by up to two orders of magnitude. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)