v 1 1 4 O ct 1 99 9 Riccati equation , Factorization Method and Shape Invariance

ua nt - p h / 99 10 00 9 v 1 3 O ct 1 99 9 Bäcklund - type superposition and free particle n - susy partners

The higher order susy partners of Schrödinger Hamiltonians can be explicitly constructed by iterating a nonlinear difference algorithm coinciding with the Bäcklund superposition principle used in soliton theory. As an example, it is applied in the construction of new higher order susy partners of the free particle potential, which can be used as a handy tool in soliton theory. Recent studies co...

Riccati equation, Factorization Method and Shape Invariance

ar X iv : h ep - t h / 99 02 19 8 v 2 2 4 O ct 1 99 9 Heisenberg and Modular Invariance of N = 2 Conformal Field Theory

We present a theta function representation of the twisted characters for the rational N=2 superconformal field theory, and discuss the Jacobi-form like functional properties of these characters for a fixed central charge under the action of a finite Heisenberg group and modular transformations.

ua nt - p h / 99 10 03 8 v 1 8 O ct 1 99 9 Refined Factorizations of Solvable Potentials

A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse and Coulomb potentials to obtain a wide set of raising and lowering operators, and to show clearly the connection that link these systems.

ar X iv : s ol v - in t / 9 90 20 05 v 2 1 4 O ct 1 99 9 Multiscale Analysis

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon ch...