Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 9, Issue Supplement 2, September 2002

Special Issue in Honour of PGL Leach on the Occasion of His 60th Birthday

Foreword
the Painlevé, the Psi Series
Pages: 36 - 48
The classical (ARS) algorithm used in the Painlevé test picks up only those functions analytic in the complex plane. We complement it with an iterative algorithm giving the leading order and the next terms in all cases. This algorithm works both for an ascending series (about a singularity at finite...
I K, F M MAHOMED, C WAFO SOH
Pages: 49 - 59
We obtain a basis of joint or proper differential invariants for the scalar linear hperbolic partial differential equation in two independent variables by the infinitesimal method. The joint invariants of the hyperbolic equation consist of combinations of the coefficients of the equation and their...
A H KARA, F M MAHOMED
Pages: 60 - 72
The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie­Bäcklund generator is extended to include any Lie­Bäcklund generator. Also, it is shown that the Lie algebra of Lie­Bäcklund symmetries of a conserved...
P G L LEACH, S É BOUQUET
Pages: 73 - 91
Cheb-Terrab and Roche (J. Sym. Comp. 27 (1999), 501­519) presented what they termed a systematic algorithm for the construction of integrating factors for second order ordinary differential equations. They showed that there were instances of odinary differential equations without Lie point symmetries...
Miloslav ZNOJIL
Pages: 122 - 133
The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resuting "effective" Hamiltonians Heff (E) are always Hermitian,...