摘要:

N-fold Bäcklund transformation for the Davey-Stewartson equation is constructed by using the analytic structure of the Lax eigenfunction in the complex eigenvalue plane. Explicit formulae can be obtained for a specified value ofN. Lastly it is shown how generalized soliton solutions are generated from the trivial ones.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.1

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The characteristic representation, or Goursat problem, for the Klein-Fock-Gordon equation with Volkov interaction [1] is regarded. It is shown that in this representation the explicit form of the Volkov propagator can be obtained. Using the characteristic representation technique, the Schwinger integral [2] in the Volkov problem can be calculated.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.2

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.3

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

We analyse the behaviour of the Dirac equation ind= 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-parameter families of solvable potentials. To illustrate the procedure in a simple but relevant context, we resort to a model which has proved useful in showing the phenomenon of fermion number fractionalization.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.4

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Abstract telegrapher’s equations and some random walks of Poisson type are shown to fit into the framework of the Hamiltonian formalism after an appropriate time-dependent rescaling of the basic variables has been made.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.5

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Infinite-dimensional algebra of all infinitesimal transformations of solutions of the self-dual Yang-Mills equations is described. It contains as subalgebras the infinite-dimensional algebras of hidden symmetries related to gauge and conformal transformations.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.6

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries satisfy various compatibility conditions. These conditions enable the discrete symmetries to be found systematically, with little effort.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.7

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A concept of asymptotic symmetry is introduced which is based on a definition of symmetry as a reducibility property relative to a corresponding invariant ansatz. It is shown that the nonlocal Lorentz invariance of the free-particle Schrödinger equation, discovered by Fushchych and Segeda in 1977, can be extended to Galilei-invariant equations for free particles with arbitrary spin and, with our definition of asymptotic symmetry, to many nonlinear Schrödinger equations. An important class of solutions of the free Schrödinger equation with improved smoothing properties is obtained.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.8

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The conventional theory of resonance broadening for a two-species plasma in a magnetic field is revised, and applied to an ionospheric turbulence case. The assumptions made in the conventional theory of resonance broadening have, in the past, led to replacing the frequencyωbyω+ik2⊥D∗in the resonant part of the linear dielectric function to obtain the nonlinear dielectric function. WhereD∗is an anomalous diffusion coefficient due solely to wave scattering of the particle orbits. We show that in general these assumptions are not valid, and consequently the straightforward substitution of frequencies is not legitimate. We remedy these problems and derive expressions for the time-dependent components of the diffusion tensor. The improved resonance broadening theory is developed in the context of an ionospheric problem, namely that of the Farley-Buneman turbulence in the auroral E-region. A kinetic description of the electrons is used. A general expression for the nonlinear dielectric function is derived in the special case where no parallel electric field is present, and the differences with the conventional dispersion relation are discussed.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.9

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The fundamental problem of Farley-Buneman turbulence in the auroralE-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroralE-region plasma has to undergo before reaching a steady state. The mode-coupling calculation, for Farley-Buneman turbulence, is developed in order to place it in perspective and to estimate its magnitude relative to the anomalous effects which arise through the nonlinear wave-particle interaction. This nonlinear effect, known as nonlinear “Landau damping” is due to the coupling of waves which produces other waves which in turn lose energy to the bulk of the particles by Landau damping. This leads to a decay of the wave energy and consequently a heating of the plasma. An equation governing the evolution of the field spectrum is derived and a physical interpration for each of its terms is provided.

ISSN:1402-9251    

DOI:10.2991/jnmp.1998.5.4.10

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor