Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations

The generalized conditional symmetry approach is applied to study the variable separation of the extended wave equations. Complete classification of those equations admitting functional separable solutions is obtained and exact separable solutions to some of the resulting equations are constructed.

Lax Connection of Strings in γ-Deformed Backgrounds

In this paper we consider classical strings propagating in γ-deformed AdS3 × S^3 backgrounds generated by TsT transformation on the AdS3 sector, which is described as the group manifold SL（2, R）, then we prove that the U（1） currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds. Using TsT transformation, we can derive the local Lax connection and the monodromy matrix in γ-deformed backgrounds with the spectral parameter, which ensures the classical integrability of the string theories.

Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient a2 〈 0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k = -1, the third order Lovelock black holes are thermodynamically stable for the whole range r＋. When k = 1, we found that the black hole has an intermediate unstable phase for D = 7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient a is under a critical value. For D ≥ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient ＆ is under a critical value for D = 8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with fiat horizon do not depend on the Loveloek coefficients and are the same as those of black holes in general gravity.

General Solutions of Reflection Equations for Bariev Model

The integrable general open-boundary conditions for the one-dimensional Bariev chain are considered. All kinds of solutions to the reflection equation （RE） and its dual are obtained.

Moduli Space of IIB Superstring and SUYM in AdS5 × S^5

This paper consists of two parts. In part I, we interpret the hidden symmetry of the moduli space of lib superstring on AdS5× S^5 in terms of the chiral embedding in AdS5, which turns out to be the CP^3 conformal affine Toda model. We review how the position μ of poles in the Riemann-Hilbert formulation of dressing transformation and the value of loop parameter μ in the vertex operator of affine algebra determine the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU（4） symmetry affinizes the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients μ of twistor. In part Ⅱ by extending the dressing symmetric a.ction of lib string in AdS5×S^5 to the D3 brane, we find a gauged WZW aztion of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structures of left and right a-planes glue into an ambitwistor. The symmetry group of Nahm equations is centrally extended to an affine group, thus we explain why the spectral curve is given by affine Toda.

Long-Lived Rogue Waves and Inelastic Interaction in Binary Mixtures of Bose–Einstein Condensates

We investigate bright,dark and two rogue waves in two-component Bose–Einstein condensates.It is found that one rogue wave of a new structure that contains two humps and two valleys around one center in the temporal-spatial distribution interacts with the conventional rogue wave.We present an effective way to obtain long-lived rogue waves through managing the nonlinear interaction with modulating trapping frequency and interchange atoms between thermal clouds and condensates.The results provide many possibilities to manipulate rogue waves experimentally in the condensate system.

Testing Quantum Entanglement with Local Measurement

We propose to detect quantum entanglement by a condition of local measurements.We find that this condition can efficiently detect the pure entangled states for both discrete and continuous variable systems.It does not depend on interference of decoherence from noise and detection loss in some systems,which allows a loophole-free test in real experiments.In particular,it is a necesary condition for the violation of some generalized Bell inequalities.

Thermodynamics of Slowly Rotating Charged Black Holes in Anti-de Sitter Einstein-Gauss-Bonnet Gravity

By using a new approach,we demonstrate the analytic expressions for slowly rotating Gauss-Bonnet charged black hole solutions with one non-vanishing angular momentum in higher-dimensional anti-de Sitter spaces.Up to linear order of the rotating parameter a,the mass,Hawking temperature and entropy of the charged black holes get no corrections from rotation.

Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target withℤ2n Grading

The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target withℤ2n grading is derived using a first−order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints.This enables us to show that the conserved charges of the theory are in involution.When n=2,our results coincide with the results given by Magro for the pure spinor description of AdS5×S5 string theory(when the ghost terms are omitted).

Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions

The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction. These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.

Exact Solutions of One-Dimensional N-Component Bariev Model with General Boundary Conditions

The N-component Bariev model for correlated hopping with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived.

Exact Solution for Perk-Schultz Model with Boundary Impurities

The Perk-Schultz model with SUq(m\n)spin boundary impurities is constructed by dressing the c-number reflecting K matrix with local L-matrix which acts non-trivially on an impurity Hilbert space.The eigenvalue of the transfer matrix and the corresponding Bethe ansatz equations with different c-number reflecting K-matrices are obtained by using the nested Bethe ansatz method(m≠n).When m=1,n=2,our results come back to that of super-symmetric t-J model with SU_(q)(1\2)spin boundary impurities.

Rational SU(N) Gaudin Model

We propose the eigenstates and eigenvalues of Hamiltonians of the rational SU(N)Gaudin model based on the quasi-classical limit of the SU(N)chain under the periodic boundary condition.Using the quantum inverse scattering method,we also obtain the eigenvalues of the generation function of the rational SU(N)Gaudin model.

Static spherically symmetric star in Gauss-Bonnet gravity

We explore static spherically symmetric stars in Gauss-Bonnet gravity without a cosmological constant, and present an exact internal solution which attaches to the exterior vacuum solution outside stars. It turns out that the presence of the Gauss-Bonnet term with a positive coupling constant completely changes thermal and gravitational energies, and the upper bound of the red shift of spectral lines from the surface of stars. Unlike in general relativity, the upper bound of the red shift is dependent on the density of stars in our case. Moreover, we have proven that two theorems for judging the stability of equilibrium of stars in general relativity can hold in Gauss-Bonnet gravity.

Dynamics of Nonautonomous Dark Solitons

We solve a generalized nonautonomous nonlinear Schrodinger equation analytically by performing the Hirota＇s bilinearization method. The precise expression of a parameter e, which provides a compatibility condition and dark soliton management, is obtained. Comparing with nonautonomous bright soliton, we find that the gain parameter affects both the background and the valley of dark soliton （∈2 ≠ 1） while it has no effects on the wave central position. Moreover, the precise expressions of a nonautonomous black soliton＇s （∈2 = 1） width, background and the trajectory of its wave central, which describe the dynamic behavior of soliton＇s evolution, are investigated analytically. Finally, the stability of the dark soliton solution is demonstrated numerically. It is shown that the main characteristic of the dark solitons keeps unchanged under a slight perturbation in the compatibility condition.