Spinor Field in Bianchi type-I Universe: regular solutions

Self-consistent solutions to the nonlinear spinor field equations in General Relativity has been studied for the case of Bianchi type-I (B-I) space-time. It has been shown that, for some special type of nonliearity the model provides regular solution, but this singularity-free solutions are attained at the cost of broken dominant energy condition in Hawking-Penrose theorem. It has also been shown that the introduction of $\Lambda$-term in the Lagrangian generates oscillations of the B-I model, which is not the case in absence of $\Lambda$ term. Moreover, for the linear spinor field, the $\Lambda$ term provides oscillatory solutions, those are regular everywhere, without violating dominant energy condition. Key words: Nonlinear spinor field (NLSF), Bianch type -I model (B-I), $\Lambda$ term PACS 98.80.C CosmologyComment: RevTex, 21 page

Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins

New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $n ($n=s-\frac12$) antisymmetric w.r.t. n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method