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1.
We apply the method of group foliation to the complex Monge-Ampère equation (CMA
2) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup ofCMA
2 to produce a foliation of the solution space into orbits of solutions with respect to this group and a corresponding splitting
ofCMA
2 into an automorphic system and a resolvent system. We propose a new approach to group foliation which is based on the commutator
algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator
representation of the resolvent system.
Presented by M.B. Sheftel at the DI-CRM Workshop held in Prague, 18–21 June 2000. 相似文献
2.
A Type II hidden symmetry of the non-linear second heavenly equation in gravitational physics is identified. Its provenance from other partial differential equations is studied. Two reductions of the second heavenly equation produce the Monge–Ampère equation in similarity variables and new analytic solutions are possible. 相似文献
3.
V.S. Gerdjikov G.G. Grahovski N.A. Kostov 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):243-248
The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat
dressing method is appropriately modified to construct their soliton solutions.
Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: gerjikov@inrne.bas.bg 相似文献
4.
E.V. Votyakov A. De Martino D.H.E. Gross 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(4):593-603
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation
for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta,
instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as
double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium
configurations against rotational symmetry breaking, and provide the global phase diagram.
Received 8 July 2002 Published online 15 October 2002
RID="a"
ID="a"e-mail: demartino@hmi.de 相似文献
5.
N.A. Kostov 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):255-259
We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed
in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for
dynamical systems related to Korteweg-de Vries equation are found.
Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: nakostov@ie.bas.bg 相似文献
6.
R. Fedele H. Schamel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):313-320
An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de
Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis
for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function,
can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the
latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the
current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation,
starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current
velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant
current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily
large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined
variable x-u0 s (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de
Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the
present paper and the ones already known in literature is also presented.
Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002 相似文献
7.
N.L. Tsintsadze P.K. Shukla L. Stenflo 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,23(1):109-115
The electroweak coupling between intense neutrino beams and strongly degenerate relativistic dense electron-positron magnetoplasmas
is considered. The intense neutrino bursts interact with the plasma due to the weak Fermi interaction force, and their dynamics
is governed by a kinetic equation. Our objective here is to develop a kinetic equation for a degenerate neutrino gas and to
use that equation to derive relativistic magnetohydrodynamic equations. The latter are useful for studying numerous collective
processes when intense neutrino beams nonlinearly interact with degenerate, relativistic, dense electron-positron plasmas
in strong magnetic fields. If the number densities of the plasma particles are of the order of 1033 cm-3, the pair plasma becomes ultra-relativistic, which strongly affects the potential energy of the weak Fermi interaction. The
new system of equations allows several neutrino-driven streaming instabilities involving new types of relativistic Alfvén-like
waves. The relevance of our investigation to the early universe and supernova explosions is discussed.
Received 11 September 2002 Published online 4 February 2003
RID="a"
ID="a"Permanent address: Department of Physics, Tbilisi State University, Chavchavadze 3, Tbilisi 38028, Georgia.
RID="b"
ID="b"Also at the Department of Plasma Physics, Ume? University, 90187 Ume?, Sweden; and the Center for Interdisciplinary Plasma Science,
Max-Planck Institut für Plasmaphysik und extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany. e-mail: ps@tp4.ruhr-uni-bochum.de
RID="c"
ID="c"Permanent address: Department of Plasma Physics, Ume?University, 90187 Ume?, Sweden. 相似文献
8.
E. Nissimov S. Pacheva 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):197-201
The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in N = 1, 2 superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable systems.
The latter are coupled systems of several multi-component non-linear Schr?dinger-like hierarchies whose basic nonlinear evolution
equations contain additional quintic and higher-derivative nonlinear terms. Also, we obtain the N = 2 supersymmetric extension of Toda chain model as Darboux-B?cklund orbit of the simplest reduced N = 2 super-KP hierarchy and find its explicit solution.
Received 13 September 2001 Published online 2 October 2002
RID="a"
ID="a"e-mail: nissimov@inrne.bas.bg
RID="b"
ID="b"e-mail: svetlana@inrne.bas.bg 相似文献
9.
P.K. Shukla R. Fedele M. Onorato N.L. Tsintsadze 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(4):613-618
The nonlinear coupling between light beams and non-resonant ion density perturbations in a plasma is considered, taking into
account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations comprising a nonlinear
Schr?dinger equation for light beams and a driven (by the light beam pressure) ion-acoustic wave response is derived. It is
shown that the stationary solutions of our nonlinear equations can be represented in the form of a bright and dark/gray soliton
for the one-dimensional problem. We also present numerical results which exhibit that our bright soliton solutions are stable
exclusively for the values of the parameters compatible with our theory.
Received 24 July 2002 Published online 31 October 2002
RID="a"
ID="a"Permanent address: Dipartimento di Scienze Fisiche, Universitá Federico II and INFN, Complesso Universitario di M.S. Angelo, Via Cintia, 80126
Napoli, Italy e-mail: renato.fedele@na.infn.it
RID="b"
ID="b"Permanent address: Dipartimento di Fisica Generale, Universitá di Torino, Via Pietro Giuria 1, 10125 Torino, Italy
RID="c"
ID="c"Permanent address: Institute of Physics, Georgian Academy of Sciences, Tbilisi 380077, Georgia 相似文献
10.
C.M. Horowitz E.V. Albano 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(4):563-569
The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's
evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the
corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on
p in the following way: ν(p) = νp and λ(p) = λp
3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation
can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp
2. It is expected that these results will help to find a framework for the development of stochastic equations starting from
microscopic details of growth models.
Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003
RID="a"
ID="a"e-mail: ealbano@inifta.unlp.edu.ar 相似文献
11.
S. Villain-Guillot C. Josserand 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):305-309
We develop a new technique describing the non linear growth of interfaces. We apply this analytical approach to the one dimensional
Cahn-Hilliard equation. The dynamics is captured through a solvability condition performed over a particular family of quasi-static
solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple
ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is
also well characterized. Numerical simulations are compared in a satisfactory way with the analytical results through three
different fitting methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.
Received 16 October 2001 / Received in final form 15 March 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: josseran@lmm.jussieu.fr
RID="b"
ID="b"UMR CNRS 7607 相似文献
12.
K. Knorr L. Ehm M. Hytha B. Winkler W. Depmeier 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(3):297-303
The high-pressure behaviour of PbS was investigated by angular dispersive X-ray powder diffraction up to pressures of 6.8
GPa. Experiments were accompanied by first principles calculations at the density functional theory level. By combining both
methods reliable data for the elastic properties of rock-salt type α- and high-pressure β-PbS could be obtained. β-PbS could be determined to crystallise in the CrB-type (B33), with space group Cmcm. The reversible ferro-elastic α/β transition is of first order. It is accompanied by a large volume discontinuity of about 5% and a coexistence region of the
two phases. A gliding mechanism of {001} bilayers along one of the cubic 〈110〉 directions governs the phase transition which can be described in terms of group/subgroup relationships via a common subgroup, despite its reconstructive character. The quadrupling of the primitive unit cell indicates a wave vector
(0, 0,π/
a
) on the Δ-line of the Brillouin zone.
Received 11 October 2002 Published online 14 February 2003
RID="a"
ID="a"Also at: Institute of Physics of the Czech Academy of Sciences, Cukrovarnicka 10, 16253 Praha 6, Czech Republic e-mail: knorr@min.uni-kiel.de
RID="b"
ID="b"Present address: University of Cambridge, Cavendish Laboratory (TCM), Madingley Road, Cambridge CB3 0HE, UK
RID="c"
ID="c"Present address: Johann-Wolfgang Goethe Universit?t, Mineralogisches Institut, Kristallographie, Senckenberganlage 30, D 60054 Frankfurt a.M.,
Germany 相似文献
13.
V. Hankevych F. Wegner 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,31(3):333-342
We present a stability analysis of the 2D t
-
t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed
numerical calculation for the various representations under the point group C
4ν
in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly
large number of phases has been observed. Some of them have an order parameter with many nodes in -space. Commonly discussed types of order found by us are antiferromagnetism, d
x2 - y2
-wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a
particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made.
Received 25 July 2002 / Received in final form 28 November 2002 Published online 14 February 2003
RID="a"
ID="a"Current address: Département de physique and Centre de recherche sur les propriétés électroniques de matériaux avancés, Université de Sherbrooke,
Sherbrooke, Québec, Canada J1K 2R1 e-mail: vaha@physique.usherb.ca 相似文献
14.
D.I. Pushkarov 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):295-300
In this work we present a full selfconsistent set of nonlinear equations which unifies the nonlinear elasticity theory equations,
the Boltzmannn transport theory and the Maxwell equations for quasiparticles with arbitrary dispersion laws in nonstationarily
deformed crystals with arbitrary (but linear) constitutive relations. Transformations to replace the Galilean ones are obtained,
the quasiparticle mechanics in a Hamiltonian form is deduced, and a Boltzmann-type transport equation (valid in the whole
Brillouin zone) is derived. The theory may be applied to metals, semiconductors, quantum crystals, low-dimensional structures
etc.
Received 20 October 2001 Published online 2 October 2002
RID="a"
ID="a"e-mail: dipushk@issp.bas.bg 相似文献
15.
M. Zamboni-Rached E. Recami H.E. Hernández-Figueroa 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,21(2):217-228
By a generalized bidirectional decomposition method, we obtain new Superluminal localized solutions to the wave equation (for
the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several of them being endowed with
finite total energy. We construct, among the others, an infinite family of generalizations of the so-called “X-shaped" waves. Results
of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics,
seismology, geophysics, gravitation, elementary particle physics, etc.).
Received 23 June 2002 Published online 24 September 2002
RID="a"
ID="a"Work partially supported by MIUR and INFN (Italy), and by FAPESP (Brazil). This paper did first appear as e-print physics/0109062
[and as preprint INFN/FM-01/02 (I.N.F.N.; Frascati, 2001)].
RID="b"
ID="b"e-mail: recami@mi.infn.it 相似文献
16.
Y. Fukumoto 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):167-171
Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the
localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius
to curvature radius, the velocity of a vortex filament is derived to O(ε3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is
found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy.
Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp 相似文献
17.
R. Metzler 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(2):249-258
A generalised random walk scheme for random walks in an arbitrary external potential field is investigated. From this concept
which accounts for the symmetry breaking of homogeneity through the external field, a generalised master equation is constructed.
For long-tailed transfer distance or waiting time distributions we show that this generalised master equation is the genesis
of apparently different fractional Fokker-Planck equations discussed in literature. On this basis, we introduce a generalisation
of the Kramers-Moyal expansion for broad jump length distributions that combines multiples of both ordinary and fractional
spatial derivatives. However, it is shown that the nature of the drift term is not changed through the existence of anomalous
transport statistics, and thus to first order, an external potential Φ(x) feeds back on the probability density function W through the classical term ∝/
x
(x)W(x, t), i.e., even for Lévy flights, there exists a linear infinitesimal generator that accounts for the response to an external field.
Received 30 June 2000 and Received in final form 12 November 2000 相似文献
18.
Extended Group Foliation Method and Functional Separation of Variables to Nonlinear Wave Equations 总被引:4,自引:0,他引:4
QU Chang-Zheng ZHANG Shun-Li 《理论物理通讯》2005,44(4):577-582
Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach. 相似文献
19.
S. Residori N. Olivi-Tran 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,17(2):255-259
In 2D optical patterns obtained in a Liquid Crystal Light Valve with optical feedback, we show a new kind of geometrical frustration
which comes from the imposed form of the boundaries. The circular section of the incoming laser beam presents a symmetry which
belongs to the O(2) group, whereas the optical feedback selects patterns with a symmetry restrained to a dihedral subgroup
of O(2). By imposing boundaries which respect the symmetry of the dihedral group, we lift the frustration and obtain perfectly
ordered patterns.
Received 19 January 2001 and Received in final form 2 June 2001 相似文献
20.
A. Borah S. Ghosh S. Nandy 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(2):221-225
The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions,
related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed.
Received 17 April 2002 Published online 2 October 2002
RID="a"
ID="a"e-mail: abhijit@iitg.ernet.in
RID="b"
ID="b"e-mail: sasanka@iitg.ernet.in
RID="c"
ID="c"e-mail: sudipta@iitg.ernet.in 相似文献