Journal of Nonlinear Mathematical Physics

Volume 8, Issue 4, November 2001

1. A Finite Dimensional Analog of the Krein Formula

I A SHERESHEVSKII
Pages: 446 - 457
I offer a simple and useful formula for the resolvent of a small rank perturbation of large matrices. I discuss applications of this formula, in particular, to analytical and numerical solving of difference boundary value problems. I present examples connected with such problems for the difference...

2. Asymptotic Approximation of Hyperbolic Weakly Nonlinear Systems

A KRYLOVAS, R CIEGIS
Pages: 458 - 470
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equtions disintegrates into independent equations for non-resonance systems. We consider the resonance conditions for some classes of solutions....

3. Least Action Principle for an Integrable Shallow Water Equation

Adrian CONSTANTIN, Boris KOLEV
Pages: 471 - 474
For an integrable shallow water equation we describe a geometrical approach shoing that any two nearby fluid configurations are successive states of a unique flow minimizing the kinetic energy.

4. Symmetry, Singularities and Integrability in Complex Dynamics V: Complete Symmetry Groups of Certain Relativistic Spherically Symmetric Systems

P G L LEACH, M C NUCCI, S COTSAKIS
Pages: 475 - 490
We show that the concept of complete symmetry group introduced by Krause (J. Math. Phys. 35 (1994), 5734­5748) in the context of the Newtonian Kepler problem has wider applicability, extending to the relativistic context of the Einstein equations dscribing spherically symmetric bodies with certain...

5. Random Groups in the Optical Waveguides Theory

G B MALYKIN, V I POZDNYAKOVA, I A SHERESHEVSKII
Pages: 491 - 517
We propose a new approach to the mathematical description of light propagation in a single-mode fiber light-guide (SMFLG) with random inhomogeneities. We investgate statistics of complex amplitudes of the electric field of light wave by methods of the random group theory. We have analyzed the behavior...

6. On Anomalies in Classical Dynamical Systems

Francesco TOPPAN
Pages: 518 - 533
The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamitonian formulation admits symmetries of the action for which the Noether conserved charges, endorsed with the Poisson bracket structure,...

7. Integrable Discretizations of Some Cases of the Rigid Body Dynamics

Yuri B SURIS
Pages: 534 - 560
A heavy top with a fixed point and a rigid body in an ideal fluid are important examples of Hamiltonian systems on a dual to the semidirect product Lie algebra e(n) = so(n) Rn . We give a Lagrangian derivation of the corresponding equations of motion, and introduce discrete time analogs of two integrable...

8. On Testing Integrability

Peter H VAN DER KAMP, Jan A SANDERS
Pages: 561 - 574
We demonstrate, using the symbolic method together with p-adic and resultant methods, the existence of systems with exactly one or two generalized symmetries. Since the existence of one or two symmetries is often taken as a sure sign (or as the definition) of integrability, that is, the existence...