Supersymmetry and classical solutions

We obtain classical solutions to the field equations of the massless supersymmetric Wess-Zumino model and to the field equations of the interacting SU(2) gauge supermultiplet. This is done by applying finite supersymmetry transformations to the known solutions of the scalar field equation with ?⁴ interaction and the Yang-Mills field equations. The relevance of supersymmetry to the solution of classical field equations involving anticommuting fermion fields is discussed.     

H-space and Robinson-Trautman solutions

It is shown that in theH-space of any Robinson-Trautman type II solution there is a uniquely defined world-line and that, under suitable regularity conditions, this world-line is a geodesic.     

变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换，构造变系数广义KdV方程的解，获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词： KdV方程 变系数广义KdV方程 类孤波解 精确解     

New multi—soliton solutions and travelling wave solutions of the dispersive long—wave equations

Using the extended homogeneous balance method,the (1 1)-dimensional dispersive long-wave equations have been solved.Starting from the homogeneous balance method,we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation.Usually,we can obtain only a type of soliton-like solution.In this paper,we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.     

一类非线性方程的compacton解及其移动compacton解

研究一类非线性方程,即广义Camassa-Holm方程C(n):ut+kux+β1u\{xxt\}+β2u\{n+1\}x+β3uxun\{xx\}+β4uun\{xxx\}=0.通过四种拟设得到丰富的精确解，特别是当k≠0时得到了com pacton解,当k=0时得到了移动compacton解.最后利用线 性化的方法得到了其他形式的广义Camassa-Holm方程的compacton解. 关键词： 广义Camassa-Holm方程 compacton解 移动compacton解     

Multiple soliton solutions and multiple singular soliton solutions for two integrable systems

Two systems of two-component integrable equations are investigated. The Cole-Hopf transformation and the Hirota's bilinear method are applied for a reliable treatment of these two systems. Multiple-soliton solutions and multiple singular soliton solutions are obtained for each system.     

Mass renormalization and runaway solutions

Zeitschrift für Physik B Condensed Matter - The relationship between negative mechanical mass and runaway solutions is studied using the model of a charged spherical shell. The model yields...     

Simplex equations and their solutions

We investigate ann-simplex generalization of the classical and quantum Yang-Baxter equation. For the case ofsl(2) we find the most general solution of the classicaln-simplex equation for alln. These classical solutions can be quantized (in the sense of quantum group theory) forn=2,3 and we exhibit a quantum solution to the tetrahedron equations (n=3). The classical nondegenerate solutions cannot be quantized forn=4.     

Multikink solutions and deformed defects

In this work we consider an application of the deformation procedure that enables us to construct, systematically, scalar field models supporting multikinks. We introduce a new deformation function in order to realize this task. We exemplify the procedure with three different starting models already known in the literature, and the resulting deformed models have rich minima structures which are responsible for the appearance of multikink configurations. We have also considered an application to braneworld scenarios, where we have obtained interesting configurations corresponding to the multikink solutions.     

Metal-ammonia solutions

In dilute solutions of alkali metals in ammonia electrons are localized in cavities in the solvent, and thermodynamic and transport properties are very similar to those found for dilute solutions of strong electrolytes. At higher concentrations the properties deviate markedly from those of electrolyte solutions and approach those of a liquid metal. In this paper we propose an explanation for cavity formation, and discuss the metal-non-metal transition in the light of recent information about the transition in vanadium oxides and doped semiconductors.     

Robinson-trautman solutions

There is an examination of the particular class of solutions of the Robinson-Trautman type, which may be interpreted as the Schwarzschild solution with weak perturbations decaying exponentially. The energy-momentum tensor of the gravitational field is used to study the multipole nature of the radiation from these systems and the temporal and spatial distributions of this radiation. It is shown that this class of solutions is a particular subclass of the solutions of Bondi et al. for axisymmetric isolated sources with radiation. An information function for the systems is found.Order of the Red Banner of the Workers.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–49, September, 1969.In conclusion the author thanks D. I. Rodichev for fruitful discussion of these results.     

两个非线性发展方程的双向孤波解与孤子解

采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解. 关键词： 齐次平衡法 孤子解 孤波解 广义Boussinesq方程 bidirectional Kaup-Kupershmi dt方程     

Multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas-Lenells equation

In this letter, we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas-Lenells equation over a nonzero background. First, we obtain 2n-soliton solutions with a nonzero background via n-fold Darboux transformation, and find that these soliton solutions will appear in pairs. Particularly, 2n-soliton solutions consist of n ‘bright' solitons and n ‘dark' solitons. This phenomenon implies a new form of integrability: even integrability. Then interactions between solitons with even numbers and breathers are studied in detail. To our best knowledge, a novel nonlinear superposition between a kink and 2n-soliton is also generated for the first time. Finally, interactions between some different smooth positons with a nonzero background are derived.     

解的移植法与含源耦合VCmKdV方程的解

根据变系数modified Korteweg-de Vries（VCmKdV）方程与常系数KdV-mKdV方程的非线性项、色散项的相似性,对解已知的KdV-mKdV方程做适当变换,并将它的解移植到解未知的VCmKdV方程,由此构造出两个不同方程解之间的移植关系.利用这种解的移植方法,求得了由两层流体模型经演化获得的含有源（或汇）耦合VCmKdV系统新的精确解和类孤波解.对Bcklund变换与解的移植法进行了比较,分析了源和汇对波幅的影响. 关键词： 解的移植法 KdV-mKdV方程 耦合VCmKdV系统 类孤波解     

A new method for constructing soliton solutions and periodic solutions of nonlinear evolution equations

With the aid of the symbolic computation, we improve Xie's algorithm [F. Xie, Z.Y. Yan, H. Zhang, Phys. Lett. A 285 (2001) 76], and present a new extended method. Based on the new general ansatz (3), we successfully solve a compound KdV-MKdV equation, and obtain some special solutions which contain soliton solutions, and periodic solutions. The method can also be applied to other nonlinear partial differential equations.     

Cosmological background solutions and cosmological backreactions

The cosmological backreaction proposal, which attempts to account for observations without a primary dark energy source in the stress-energy tensor, has been developed and discussed by means of different approaches. Here, we focus on the concept of cosmological background solutions in order to develop a framework to study different backreaction proposals.     

Rindler solutions and their physical interpretation

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded. Zh. éksp. Teor. Fiz. 114, 777–785 (September 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Homothetic motions and vacuum Robinson-Trautman solutions

The approach to symmetries given by Kerr and Debney (1970) is applied to the class of vacuum Robinson-Trautman solutions. The coordinate freedom is extended and used to define the pull-backs of local diffeomorphisms which are then shown to be homothetic motions. The resulting homothetic Killing's equations are solved to give a form of all homothety groups for this class.     

Droplets evaporation: Problems and solutions

The evaporation of single droplets and sprays into gaseous atmosphere and the evaporation of sessile liquid droplets on solid substrates are here considered. We argue that if thermodynamics is augmented with Derjaguin’s (disjoining/conjoining) pressure to handle phenomena in a vicinity of the three-phase contact line, problems like the singularity of the evaporation flux and of the viscous stress at the three-phase contact line of a sessile droplet are ruled out.