Exact Bosonic Solutions of the Truncated Skyrme Model

A model defined by half the Lagrangian （the highly nonlinear part） of the Skyrme model is investigated. Two classes of bosonic solutions are obtained. It is shown that, although the field configurations of these two classes are different, the energy densities for the two classes take the same form.     

On Finding Global Smooth Solutions to the Landau-Lifshitz Equation

We prove that n-dimensional radial symmetric Landau-Lifshitz equation possesses at least two classes of global smooth solutions with suitable initial-boundary conditions.     

On the multi-spin magnon and spike solutions from membranes

Recently important classes of solitonic string solutions were obtained—giant magnons and single spikes. In previous study we showed the existence of giant magnon-like membrane solutions and studied their properties. In this paper we investigate classical rotating membranes representing analog of a specific class of string spiky solutions. Using the reduction to the Neumann–Rosochatius integrable system we find analog of the string single spike solutions. In contrast to the magnon-like solutions, this case is characterized with finite difference of energy and “winding number” and finite spins as well.     

Exactly Solvable Combinations of Scalar and Vector Potentials for the Dirac Equation Interrelated by Riccati Equations

New classes of solvable scalar and vector potentials for the Dirac equation are obtained, together with the associated exact Dirac spinors. The method of derivation is based on an a priori constraint between the solutions, leading to an interrelation between the scalar and vector potential in the form ofa Riccati equation. The present note generalizes a series of former articles.     

Moving curves of the sine-Gordon equation: New links

We provide a general scheme for mapping integrable nonlinear partial differential equations of real functions to moving space curves using an approach different from the one proposed by Lamb. We apply our method to the sine-Gordon equation and obtain links to five new classes of space curves, in addition to the two found by Lamb. For each class, we display the rich variety of moving curves associated with the one-soliton, the breather, the two-soliton and the soliton-antisoliton solutions, and suggest possible applications. Our results also provide new insights with regard to the two-soliton (soliton-antisoliton) scattering process.     

Solutions of five-dimensional general relativity without spatial symmetry

Conformastationary solutions of the five-dimensional vacuum Einstein equations, depending on one or two harmonic potentials, are constructed. The solutions depending on one potential fall in three distinct classes. Solutions of two of these classes may be combined to yield a class of solutions depending on two potentials, which correspond to the Israel-Wilson-Perjès solutions of the Einstein-Maxwell theory. The asymptotically flat solutions of this class describe systems of rotating electric or magnetic monopoles.     

Entanglement dynamics under decoherence: from qubits to qudits

We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.     

Seiberg--Witten Monopoles in Three Dimensions

Dimensional reduction of the Seiberg--Witten equations leads to the equations of motion of a U(1) Chern--Simons theory coupled to a massless spinorial field. A topological quantum field theory is constructed for the moduli space of gauge equivalence classes of solutions of these equations. The Euler characteristic of the moduli space is obtained as the partition function which yields an analogue of Casson's invariant.A mathematically rigorous definition of the invariant isdeveloped for homology spheres using the theory of spectral flow ofself-adjoint Fredholm operators.     

On multivortex solutions of the weierstrass representation

The connection between the complex sine-Gordon equation on the plane associated with a Weierstrass-type system and the possibility of constructing several classes of multivortex solutions is discussed in detail. It is shown that the amplitudes of these vortex solutions represented in polar coordinates satisfy the fifth Painlevé equation. We perform the analysis using the known relations for the Painlevé equations and construct explicit formulas in terms of the Umemura polynomials, which are τ functions for rational solutions to the third Painlevé equation. New classes of multivortex solutions to the Weierstrass system are obtained through the use of this proposed procedure.     

A study on relativistic lagrangian field theories with non-topological soliton solutions

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call “admissible” models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.     

Bianchi type V perfect-fluid space-times

A method is presented to generate exact solutions of the Einstein field equations in Bianchi type V space-times. The energy-momentum tensor is of perfect fluid type. Starting from particular solutions, new classes of solutions are obtained. The geometrical and physical properties of a class of solutions are discussed.     

Scalings for a Ballistic Aggregation Equation

We consider a mean field type equation for ballistic aggregation of particles whose density function depends both on the mass and momentum of the particles. For the case of a constant aggregation rate we prove the existence of self-similar solutions and the convergence of more general solutions to them. We are able to estimate the large time decay of some moments of general solutions or to build some new classes of self-similar solutions for several classes of mass and/or momentum dependent rates.     

On Classes of Lie Solutions of MHD Equations,Expressed via the General Solution of the Heat Equation

Abstract

Large classes of Lie solutions of the MHD equations describing the flows of a viscous homogeneous incompressible fluid of finite electrical conductivity are constructed. These classes contain a number of arbitrary functions of time and the general solutions of the heat equation.     

The Analytical Solutions of 2D Stationary Broadwell Kinetic Model

The present communication is devoted to the calculation of some explicit stationary solutions of the four-velocity Broadwell kinetic model in two spatial dimensions. The method of the truncated Painlevé expansion is employed and two classes of solutions are constructed. It is shown that these solutions satisfy the special boundary value problem in a rectangle.     

Boundary Yang-Baxter equation in the RSOS/SOS representation

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and nondiagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins, respectively. Applied to (1 + 1)-dimensional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.     

四维Minkowski空间中具有立方非线性复标量场方程的平面与球面波解

本文在四维Minkowski空间中对具有立方非线性复标量场方程进行了研究,并给出了场方程的两种精确解,这两种解相当于场的平面与球面波解。 关键词：     

Relativistic compact objects in isotropic coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati-type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic-type fluid with an equation of statep =γρ is discussed in detail.     

Applications of elliptic functions to ion-acoustic plasma waves

New several classes of exact solutions are obtained in terms of the Weierstrass elliptic function for some nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. The Weierstrass elliptic function solutions of the Schamel equation, a fifth order dispersive wave equation and the Kawahara equation are constructed. Moreover, Jacobi elliptic function solutions and solitary wave solutions of the Schamel equation are also given. The stability of some periodic wave solutions is computationally studied.     

On some classes of exact solutions of scalar Born-Infeld equation

Some classes of exact solutions of scalar Born-Infeld equation have been found. Certain selected properties of these solutions have been presented.     

Three-dimensional stationary cyclic symmetric Einstein–Maxwell solutions; black holes

From a general metric for stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the (2 + 1)-dimensional gravity the uniqueness of wide families of exact solutions is established. Among them, all uniform electromagnetic solutions possessing electromagnetic fields with vanishing covariant derivatives, all fields having constant electromagnetic invariants F_μνF^μν and T_μνT^μν, the whole classes of hybrid electromagnetic solutions, and also wide classes of stationary solutions are derived for a third-order nonlinear key equation. Certain of these families can be thought of as black hole solutions. For the most general set of Einstein–Maxwell equations, reducible to three nonlinear equations for the three unknown functions, two new classes of solutions – having anti-de Sitter spinning metric limit – are derived. The relationship of various families with those reported by different authors’ solutions has been established. Among the classes of solutions with cosmological constant a relevant place is occupied by the electrostatic and magnetostatic Peldan solutions, the stationary uniform and spinning Clement classes, the constant electromagnetic invariant branches with the particular Kamata–Koikawa solution, the hybrid cyclic symmetric stationary black hole fields, and the non-less important solutions generated via SL(2,R)-transformations where the Clement spinning charged solution, the Martinez–Teitelboim–Zanelli black hole solution, and Dias–Lemos metric merit mention.