Variable-Coefficient Mapping Method Based on Elliptical Equation and Exact Solutions to Nonlinear SchrSdinger Equations with Variable Coefficient

In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schrodinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.     

Bethe-Salpeter equation with the sine-Gordon interaction

An attempt is made to study the interaction Hamiltonian,H _int =Gψ ²(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit. We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n ⁶, wheren is the principal quantum number.     

Jacobian Elliptic Function Method and Solitary Wave Solutions for Hybrid Lattice Equation

In this paper, we have successfully extended the Jacobian elliptic function expansion approach to nonlinear differential-difference equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively.     

The Kerr Solution on Partially Degenerate Hyperelliptic Riemann Surfaces

The Kerr solution for a rotating black hole can be constructed as the solitonic limit of Korotkin's theta-functional solutions of the Ernst equation on a genus-two surface. We show here that the Kerr solution can also be obtained on a partially degenerate hyperelliptic Riemann surface of arbitrary even genus.     

Shape and location of multiple charge carriers in linear π‐electron systems

We have performed a quantum‐mechanical study of a series of neutral polyenes, their multiply charged ions, and related ionic polymethines with a closed electron shell, using different methods/basis with/without electron correlations. The study shows that a multiple injection of charge carriers into a collective system of π‐electrons causes a formation of distinctive electron levels in the energy gap along with a simultaneous regular gap shift in accordance to the number of injected carriers. Each charge generates its own solitonic electron density alternation wave on adjacent carbon atoms, as well as similar bond length and valence angle alternation waves. Established regularities in charge distribution and variations of bond lengths and valence angles may be used in the molecular design of organic semiconducting materials. © 2013 Wiley Periodicals, Inc.