Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 4, Issue 3-4, September 1997
R. JACKIW
Pages: 261 - 270
I analyze the one-dimensional, cubic Schrödinger equation with a nonlinearity constructed from the current density rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one direction. Relation to the higher-dimensional Chern­Simons theory is...
Asao ARAI
Pages: 338 - 349
In models of a quantum harmonic oscillator coupled to a quantum field with a quadratic interaction, embedded eigenvalues of the unperturbed system may be unstable under the perturbation given by the interaction of the oscillator with the quantum field. A general mathematical structure underlying this...
Masayoshi TAJIRI, Yosuke WATANABE
Pages: 350 - 357
An inclined periodic soliton solution can be expressed as imbricate series of rational soliton solutions. A convenient form of the imbrication is given by using the bilinear form. A lattice soliton solution which propagaties in any direction can be also constructed by doubly imbricating rational solitons.
W.W. ZACHARY
Pages: 377 - 382
The solution of the three-dimensional free Schrödinger equation due to W.M. Shtelen based on the invariance of this equation under the Lorentz Lie algebra so(1,3) of nonlocal transformations is considered. Various properties of this solution are examined, including its extension to n 3 spatial dimensions...
Tepper L. GILL, W.W. ZACHARY
Pages: 418 - 425
We show that Maxwell's equations have a generalization associated with the propertime of the source and a new invariance group which leaves this variable fixed for all observers. We show that the second postulate (of Einstein) depends on the anthropocentric view that the only clock to use is the proper-clock...
R.Z. ZHDANOV, W.I. FUSHCHYCH
Pages: 426 - 435
We have constructed new realizations of the Galilei group and its natural extensions by Lie vector fields. These realizations together with the ones obtained by Fushchych & Cherniha (Ukr. Math. J., 1989, 41, N 10, 1161; N 12, 1456) and Rideau & Winternitz (J. Math. Phys., 1993, 34, 558) give a complete...
Jiri NIEDERLE, Anatolii NIKITIN
Pages: 436 - 444
New algebras of symmetries of the Dirac equation are presented, which are formed by linear and antilinear first­order differential operators. These symmetries are applied to decouple the Dirac equation for a charged particle interacting with an external field.
A.F. BARANNYK
Pages: 445 - 454
Subalgebras of the Lie algebra AC(2, 2) of the group C(2, 2), which is the group of conformal transformations of the pseudo-Euclidean space R2,2, are studied. All subalgebras of the algebra AC(2, 2) are splitted into three classes, each of those is characterized by the isotropic rank 0, 1, or 3. We...
A.K. PRYKARPATSKY, O.E. HENTOSH, D.L. BLACKMORE
Pages: 455 - 469
The Moser type reductions of modified Boussinessq and super-Korteweg-de Vries equations upon the finite-dimensional invariant subspaces of solutions are considered. For the Hamiltonian and Liouville integrable finite-dimensional dynamical systems concerned with the invariant subspaces, the Lax representations...
W.I. FUSHCHYCH, Z.I. SYMENOH
Pages: 470 - 479
We study symmetry properties of the heat equation with convection term (the equation of convection diffusion) and the Schrödinger equation with convection term. We also investigate the symmetry of systems of these equations with additional conditions for potentials. The obtained results are applied...