Journal of Nonlinear Mathematical Physics

Volume 5, Issue 4, November 1998
Research Article

1. On the Analytical Approach to the N-Fold Bäcklund Transformation of Davey-Stewartson Equation

Pages: 349 - 356
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 of N. Lastly it is shown how generalized soliton solutions are generated from...
Research Article

2. Fundamental Solution of the Volkov Problem (Characteristic Representation)

Pages: 357 - 363
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...
Research Article

3. Differential Constraints Compatible with Linearized Equations

Pages: 364 - 370
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
Research Article

4. Solving Simultaneously Dirac and Ricatti Equations

Pages: 371 - 382
We analyse the behaviour of the Dirac equation in d = 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,...
Research Article

5. On Infinitesimal Symmetries of the Self-Dual Yang-Mills Equations

Pages: 396 - 404
Infinite-dimensional algebra of all infinitesimal transformations of solutions of the self-dual Yang-Mills equations is described. It contains as subalgebras the infinitedimensional algebras of hidden symmetries related to gauge and conformal transformations.
Research Article

6. How to Find Discrete Contact Symmetries

Peter E. HYDON
Pages: 405 - 416
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...
Research Article

7. On Asymptotic Nonlocal Symmetry of Nonlinear Schrödinger Equations

Pages: 417 - 437
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...
Research Article

8. Resonance Broadening Theory of Farley-Buneman Turbulence in the Auroral E-Region

Pages: 438 - 461
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 frequency by + ik2 D in the resonant...
Research Article

9. Mode-Coupling and Nonlinear Landau Damping Effects in Auroral Farley-Buneman Turbulence

Pages: 462 - 470
The fundamental problem of Farley-Buneman turbulence in the auroral E-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 auroral E-region plasma has to undergo before reaching a steady state. The mode-coupling...
Research Article

10. Remarks on Random Evolutions in Hamiltonian Representation

Pages: 483 - 495
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 timedependent rescaling of the basic variables has been made.